nonlocality asymmetry and distinguishing bipartite states entanglement is a useful resource because some global operations cannot be locally implemented using classical communication we prove a number of results about what is and what is not locally possible we focus on orthogonal states which can always be globally distinguished we establish the necessary and sufficient conditions for a general set of 2 ifmmode times else texttimes fi 2 quantum states to be locally distinguishable and for a general set of 2 ifmmode times else texttimes fi n quantum states to be distinguished given an initial measurement of the qubit these results reveal a fundamental asymmetry to nonlocality which is the origin of nonlocality without entanglement and we present a very simple proof of this phenomenon

local distinguishability of quantum states in infinite dimensional systems we investigate local distinguishability of quantum states by use of convex analysis of joint numerical range of operators on a hilbert space we show that any two orthogonal pure states are distinguishable by local operations and classical communications even for infinite dimensional systems an estimate of the local discrimination probability is also given for some families of more than two pure states

distribution of bipartite entanglement for random pure states we calculate analytic expressions for the distribution of bipartite entanglement for pure random quantum states all moments of the purity distribution are derived and an asymptotic expansion for the distribution itself is deduced an approximate expression for moments and distribution of meyer wallach entanglement for random pure states is then obtained

characterizing locally indistinguishable orthogonal product states bennett physical review a vol 59 no 2 p 1070 1999 identified a set of orthogonal product states in the hilbert space bbc 3 otimes bbc 3 such that reliably distinguishing those states requires nonlocal quantum operations while more examples have been found for this counterintuitive ldquononlocality without entanglementrdquo phenomenon a complete and computationally verifiable characterization for all such sets of states remains unknown in this paper we give such a characterization for both bbc 3 otimes bbc 3 and bbc 2 otimes bbc 2 otimes bbc 2 as a consequence we show that in both spaces there is no additional set of a fundamentally different structure than those of the known instances

on state versus channel quantum extension problems exact results for u otimes u otimes u symmetry we develop a framework which unifies seemingly different extension or joinability problems for bipartite quantum states and channels this includes known extension problems such as optimal quantum cloning and quantum marginal problems as special instances central to our generalization is a variant of the jamiolkowski isomorphism between bipartite states and linear transformations which we term the homocorrelation map in contrast to the better known choi isomorphism which emphasizes the preservation of the positivity constraint use of the jamiolkowski isomorphism allows one to characterize the preservation of the statistical correlations of bipartite states and quantum channels the resulting homocorrelation map thus acquires a natural operational interpretation we define and analyze state joining channel joining and local positive joining problems in three party settings with collective symmetry obtaining exact analytical characterizations in low dimensions we find that bipartite quantum states are limited in the degree to which their measurement outcomes may agree whereas quantum channels are limited in the degree to which their measurement outcomes may disagree loosely speaking quantum mechanics enforces an upper bound on the strength of positive correlation across two subsystems at a single time as well as on the strength of negative correlation between the state of a single system across two instants of time we argue that these general statistical bounds inform the quantum joinability limitations and show that they are in fact sufficient for the three party invariant setting

kerdock codes determine unitary 2 designs the non linear binary kerdock codes are known to be gray images of certain extended cyclic codes of length n 2 m over mathbb z 4 we show that exponentiating these mathbb z 4 valued codewords by i triangleq sqrt 1 produces stabilizer states that are quantum states obtained using only clifford unitaries these states are also the common eigenvectors of commuting hermitian matrices forming maximal commutative subgroups mcs of the pauli group we use this quantum description to simplify the derivation of the classical weight distribution of kerdock codes next we organize the stabilizer states to form n 1 mutually unbiased bases and prove that automorphisms of the kerdock code permute their corresponding mcs thereby forming a subgroup of the clifford group when represented as symplectic matrices this subgroup is isomorphic to the projective special linear group psl 2 n we show that this automorphism group acts transitively on the pauli matrices which implies that the ensemble is pauli mixing and hence forms a unitary 2 design the kerdock design described here was originally discovered by cleve et al 2016 but the connection to classical codes is new which simplifies its description and translation to circuits significantly sampling from the design is straightforward the translation to circuits uses only clifford gates and the process does not require ancillary qubits finally we also develop algorithms for optimizing the synthesis of unitary 2 designs on encoded qubits i e to construct logical unitary 2 designs software implementations are available at https github com nrenga symplectic arxiv18a which we use to provide empirical gate complexities for up to 16 qubits

comparison techniques for random walk on finite groups we develop techniques for bounding the rate of convergence of a symmetric random walk on a finite group to the uniform distribution the techniques gives bounds on the second largest and other eigenvalues in terms of the eigenvalues of a comparison chain with known eigenvalues the techniques yield sharp rates for a host of previously intractable problems on the symmetric group

when do local operations and classical communication suffice for two qubit state discrimination in this paper we consider the conditions under which a given ensemble of two qubit states can be optimally distinguished by local operations and classical communication locc we begin by completing the perfect distinguishability problem of two qubit ensembles both for separable operations and locc by providing necessary and sufficient conditions for the perfect discrimination of one pure and one mixed state then for the well known task of minimum error discrimination it is shown that almost all two qubit ensembles consisting of three pure states cannot be optimally discriminated using locc this is surprising considering that any two pure states can be distinguished optimally by locc special attention is given to ensembles that lack entanglement and we prove an easy sufficient condition for when a set of three product states cannot be optimally distinguished by locc thus providing new examples of the phenomenon known as non locality without entanglement we next consider an example of n parties who each share the same state but who are ignorant of its identity the state is drawn from the rotationally invariant trine ensemble and we establish a tight connection between the n copy ensemble and shor s lifted single copy ensemble for any finite n we prove that optimal identification of the states cannot be achieved by locc however as n locc can indeed discriminate the states optimally this is the first result of its kind finally we turn to the task of unambiguous discrimination and derive new lower bounds on the locc inconclusive probability for symmetric states when applied to the double trine ensemble this leads to a rather different distinguishability character than when the minimum error probability is considered

representations of the multi qubit clifford group the q qubit clifford group that is the normalizer of the q qubit pauli group in u 2q is a fundamental structure in quantum information with a wide variety of applications we characterize all irreducible subrepresentations of the two copy representation 2 of the clifford group on the two fold tensor product of the space of linear operators m2q 2 in the companion paper helsen et al e print arxiv 1701 04299 2017 we apply this result to improve the statistics of randomized benchmarking a method for characterizing quantum systems

scaling behavior of the conserved transfer threshold process we analyze numerically the critical behavior of an absorbing phase transition in the conserved transfer threshold process we determined the steady state scaling behavior of the order parameter as a function of both the control parameter and an external field conjugated to the order parameter the external field is realized as a spontaneous creation of active particles which drives the system away from criticality the obtained results yield that the conserved transfers threshold process belongs to the universality class of absorbing phase transitions in a conserved field

quantum data hiding we expand on our work on quantum data hiding hiding classical data among parties who are restricted to performing only local quantum operations and classical communication locc we review our scheme that hides one bit between two parties using bell 1964 states and we derive upper and lower bounds on the secrecy of the hiding scheme we provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme we give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement a candidate data hiding scheme that does not use entanglement is presented we show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme

tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state we consider asymptotic hypothesis testing or state discrimination with asymmetric treatment of errors between an arbitrary fixed bipartite pure state psi rangle and the white noise state the completely mixed state under one way local operations and classical communications locc two way locc and separable positive operator valued measures povms as a result we derive the hoeffding bounds under two way locc povms and separable povms further we derive stein s lemma type of optimal error exponents under one way locc two way locc and separable povms up to the third order which clarifies the difference between one way and two way locc povm our results clarify the relationship between the entanglement of renyi entropy and the hypothesis testing under locc since the entanglement of renyi entropy appears in the formula of both the hoeffding bounds and stein s lemma type of error exponents this paper gives a very rare example in which the optimal performance under the infinite round two way locc is also equal to that under separable operations and can be attained with two round communication but not with the one way locc

asymptotic state discrimination and a strict hierarchy in distinguishability norms in this paper we consider the problem of discriminating quantum states by local operations and classical communication locc when an arbitrarily small amount of error is permitted this paradigm is known as asymptotic state discrimination and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic locc we use this new criterion to prove a gap in the locc and separable distinguishability norms we then turn to the operational advantage of using two way classical communication over one way communication in locc processing with a simple two qubit product state ensemble we demonstrate a strict majorization of the two way locc norm over the one way norm

local hypothesis testing between a pure bipartite state and the white noise state in this paper we treat a local discrimination problem in the framework of asymmetric hypothesis testing we choose a known bipartite pure state psi rangle as an alternative hypothesis and the completely mixed state as a null hypothesis as a result we analytically derive an optimal type 2 error and an optimal positive operator valued measure povm for one way local operations and classical communication locc povm and separable povm for two way locc povm we study a family of simple three step locc protocols and show that the best protocol in this family has strictly better performance than any one way locc protocol in low dimensional systems when there may exist differences between two way locc povm and one way locc povm

exponential decay of correlations implies area law we prove that a finite correlation length i e exponential decay of correlations implies an area law for the entanglement entropy of quantum states defined on a line the entropy bound is exponential in the correlation length of the state thus reproducing as a particular case hastings s proof of an area law for groundstates of 1d gapped hamiltonians

faithful squashed entanglement squashed entanglement is a measure for the entanglement of bipartite quantum states in this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states this implies that squashed entanglement is faithful that is it is strictly positive if and only if the state is entangled we derive the lower bound on squashed entanglement from a lower bound on the quantum conditional mutual information which is used to define squashed entanglement the quantum conditional mutual information corresponds to the amount by which strong subadditivity of von neumann entropy fails to be saturated our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality the proof is based on two recent results from quantum information theory the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing the distance to the set of separable states is measured in terms of the locc norm an operationally motivated norm giving the optimal probability of distinguishing two bipartite quantum states each shared by two parties using any protocol formed by local quantum operations and classical communication locc between the parties a similar result for the frobenius or euclidean norm follows as an immediate consequence the result has two applications in complexity theory the first application is a quasipolynomial time algorithm solving the weak membership problem for the set of separable states in locc or euclidean norm the second application concerns quantum merlin arthur games here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to locc operations thereby providing a new characterisation of the complexity class qma

conserved lattice gas model with infinitely many absorbing states in one dimension the conserved lattice gas model with infinitely many absorbing states is studied on a chain and on a ladder in both one dimensional lattices it exhibits a phase transition from an absorbing phase to an active state the model defined on a chain is solved exactly and shows a critical behavior with classical critical exponents however the model defined on a ladder shows a critical behavior obtained from numerical simulation that places the model in the same universality class as the manna model

general paradigm for distilling classical key from quantum states in this paper we develop a formalism for distilling a classical key from a quantum state in a systematic way expanding on our previous work on a secure key from bound entanglement horodecki et al 2005 more detailed proofs discussion and examples are provided of the main results namely we demonstrate that all quantum cryptographic protocols can be recast in a way which looks like entanglement theory with the only change being that instead of distilling einstein podolsky rosen epr pairs the parties distill private states the form of these general private states are given and we show that there are a number of useful ways of expressing them some of the private states can be approximated by certain states which are bound entangled thus distillable entanglement is not a requirement for a private key we find that such bound entangled states are useful for a cryptographic primitive we call a controlled private quantum channel pqc we also find a general class of states which have negative partial transpose are npt but which appear to be bound entangled the relative entropy distance is shown to be an upper bound on the rate of a key this allows us to compute the exact value of a distillable key for a certain class of private states

ultimate data hiding in quantum mechanics and beyond the phenomenon of data hiding i e the existence of pairs of states of a bipartite system that are perfectly distinguishable via general entangled measurements yet almost indistinguishable under locc is a distinctive signature of nonclassicality the relevant figure of merit is the maximal ratio called data hiding ratio between the distinguishability norms associated with the two sets of measurements we are comparing typically all measurements vs locc protocols for a bipartite n times n quantum system it is known that the data hiding ratio scales as n i e the square root of the real dimension of the local state space of density matrices we show that for bipartite n a times n b systems the maximum data hiding ratio against locc protocols is theta left min n a n b right this scaling is better than the previously obtained upper bounds o left sqrt n a n b right and min n a 2 n b 2 and moreover our intuitive argument yields constants close to optimal in this paper we investigate data hiding in the more general context of general probabilistic theories gpts an axiomatic framework for physical theories encompassing only the most basic requirements about the predictive power of the theory the main result of the paper is the determination of the maximal data hiding ratio obtainable in an arbitrary gpt which is shown to scale linearly in the minimum of the local dimensions we exhibit an explicit model achieving this bound up to additive constants finding that quantum mechanical data hiding ratio is only of the order of the square root of the maximal one our proof rests crucially on an unexpected link between data hiding and the theory of projective and injective tensor products of banach spaces finally we develop a body of techniques to compute data hiding ratios for a variety of restricted classes of gpts that support further symmetries

asymmetric quantum codes constructions bounds and performance recently quantum error correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit and phase flip errors an example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel where the probabilities of bit and phase flips can be related to relaxation and dephasing time respectively we study asymmetric quantum codes that are obtained from the calderbank shor steane css construction for such codes we derive upper bounds on the code parameters using linear programming a central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes for instance we derive asymmetric codes using a combination of bose chaudhuri hocquenghem bch and finite geometry low density parity check ldpc codes we show that the asymmetric quantum codes offer two advantages namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allow a higher performance when compared with symmetric codes of comparable rates our approach is based on a css construction that combines bch and finite geometry ldpc codes

realizing a 2 d positive operator valued measure by local operations and classical communication we study the realization of a 2 d positive operator valued measure povm by local operations and classical communication locc we derive that any povm on a 2 d hilbert space in which each party s space is finite dimensional can be realized by one way locc this implies that any optimal discrimination of quantum states spanning such a 2 d hilbert space is possible by one way locc regardless of the optimality criterion used and how entangled the states are

distinguishability of quantum states by positive operator valued measures with positive partial transpose we study the distinguishability of bipartite quantum states by positive operator valued measures with positive partial transpose ppt povms the contributions of this paper include 1 we give a negative answer to an open problem of showing a limitation of a previous known method for detecting nondistinguishability 2 we show that a maximally entangled state and its orthogonal complement no matter how many copies are supplied cannot be distinguished by the ppt povms even unambiguously this result is much stronger than the previous known ones and 3 we study the entanglement cost of distinguishing quantum states it is proved that 2 3 00 1 3 11 is sufficient and necessary for distinguishing three bell states by the ppt povms an upper bound of entanglement cost of distinguishing a d d pure state and its orthogonal complement is obtained for separable operations based on this bound we are able to construct two orthogonal quantum states which cannot be distinguished unambiguously by separable povms but finite copies would make them perfectly distinguishable by local operations and classical communication we further observe that a two qubit maximally entangled state is always enough for distinguishing a d d pure state and its orthogonal complement by the ppt povms no matter the value of d in sharp contrast an entangled state with schmidt number at least d is always needed for distinguishing such two states by separable povms as an application we show that the entanglement cost of distinguishing a d d maximally entangled state and its orthogonal complement must be a maximally entangled state for d 2 which implies that teleportation is optimal and in general it could be chosen as o logd d

on quantum error correction by classical feedback in discrete time we consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment for discrete time markovian evolutions in the case of fixed measurement on the environment we give criteria for quantum information to be perfectly corrigible and characterize the related feedback then we analyze the case when perfect correction is not possible and in the qubit case we find optimal feedback maximizing the channel fidelity

discord of response the presence of quantum correlations in a quantum state is related to the state s response to local unitary perturbations such a response is quantified by the distance between the unperturbed and perturbed states minimized with respect to suitably identified sets of local unitary operations in order to be a bona fide measure of quantum correlations the distance function must be chosen among those that are contractive under completely positive and trace preserving cptp maps the most relevant instances of such physically well behaved metrics include the trace the bures and the hellinger distance to each of these metrics one can associate the corresponding discord of response namely the trace or hellinger or bures minimum distance from the set of unitarily perturbed states all these three discords of response satisfy the basic axioms for a proper measure of quantum correlations in the present work we focus in particular on the bures distance which enjoys the unique property of being both riemannian and contractive under cptp maps and admits important operational interpretations in terms of state distinguishability we compute analytically the bures discord of response for two qubit states with maximally mixed marginals and we compare it with the corresponding bures geometric discord namely the geometric measure of quantum correlations defined as the bures distance from the set of classical quantum states finally we investigate and identify the maximally quantum correlated two qubit states according to the bures discord of response these states exhibit a remarkable nonlinear dependence on the global state purity

randomizing quantum states constructions and applications the construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver we show that if only near perfect security is required the size of the key can be reduced by a factor of two more specifically we show that there exists a set of roughly d log d unitary operators whose average effect on every input pure state is almost perfectly randomizing as compared to the d2 operators required to randomize perfectly aside from the private quantum channel variations of this construction can be applied to many other tasks in quantum information processing we show for instance that it can be used to construct locc data hiding schemes for bits and qubits that are much more efficient than any others known allowing roughly log d qubits to be hidden in 2 log d qubits the method can also be used to exhibit the existence of quantum states with locked classical correlations an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key our construction also provides the basic building block for a method of remotely preparing arbitrary d dimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement

on the existence of locc distinguishable bases in three dimensional subspaces of bipartite 3 n systems we present numerical evidence showing that any three dimensional subspace of c 3 c n has an orthonormal basis which can be reliably distinguished using one way locc local operations and classical communication where a measurement is made first on the three dimensional part and the result used to select an optimal measurement on the n dimensional part we also show that the order of measurement is essential by providing an example of a three dimensional subspace of c 3 c 5 which does not have any basis that can be distinguished by measuring first on the five dimensional factor

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding we consider the problem of ambiguous discrimination of two quantum states when we are only allowed to perform a restricted set of measurements let the bias of a povm be defined as the total variational distance between the outcome distributions for the two states to be distinguished the performance of a set of measurements can then be defined as the ratio of the bias of this povm and the largest bias achievable by any measurements we first provide lower bounds on the performance of various povms acting on a single system such as the isotropic povm and spherical 2 and 4 designs and show how these bounds can lead to certainty relations furthermore we prove lower bounds for several interesting povms acting on multipartite systems such as the set of local povms povms which can be implemented using local operations and classical communication locc separable povms and finally povms for which every bipartition results in a measurement having positive partial transpose ppt in particular our results show that a scheme of terhal et al for hiding data against local operations and classical communication 31 has the best possible dimensional dependence

unitary 2 designs from random x and z diagonal unitaries unitary 2 designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries often referred to as haar random unitaries they are used in a wide variety of theoretical and practical quantum information protocols and also have been used to model the dynamics in complex quantum many body systems here we show that unitary 2 designs can be approximately implemented by alternately repeating random unitaries diagonal in the pauli z basis and pauli x basis we also provide a converse about the number of repetitions needed to achieve unitary 2 designs these results imply that the process after l repetitions achieves a d l approximate unitary 2 design based on the construction we further provide quantum circuits that efficiently implement approximate unitary 2 designs although a more efficient implementation of unitary 2 designs is known our quantum circuit has its own merit that it is divided into a constant number of commuting parts which enables us to apply all commuting gates simultaneously and leads to a possible reduction of an actual execution time we finally interpret the result in terms of the dynamics generated by time dependent hamiltonians and provide for the first time a random disordered time dependent hamiltonian that generates a unitary 2 design after switching interactions only a few times unitary 2 designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries often referred to as haar random unitaries they are used in a wide variety of theoretical and practical quantum information protocols and also have been used to model the dynamics in complex quantum many body systems here we show that unitary 2 designs can be approximately implemented by alternately repeating random unitaries diagonal in the pauli z basis and pauli x basis we also provide a converse about the number of repetitions needed to achieve unitary 2 designs these results imply that the process after l repetitions achieves a d l approximate unitary 2 design based on the construction we further provide quantum circuits that efficiently implement approximate unitary 2 designs although a more efficient implementation of unitary 2 designs is known our quantum circuit has its own merit that it is divided into a constant number of commuting parts which

bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication we show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally the number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement a similar general condition is also shown for pure and mixed states these results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement

limitations of semidefinite programs for separable states and entangled games semidefinite programs sdps are a framework for exact or approximate optimization with widespread application in quantum information theory we introduce a new method for using reductions to construct integrality gaps for sdps meaning instances where the sdp value is far from the true optimum these are based on new limitations on the sum of squares sos hierarchy in approximating two particularly important sets in quantum information theory where previously no omega 1 round integrality gaps were known integrality gaps for the 2 rightarrow 4 norm had previously been sought due to its connection to small set expansion sse and unique games ug in both cases no go theorems were previously known based on computational assumptions such as the exponential time hypothesis eth which asserts that 3 sat requires exponential time to solve our unconditional results achieve the same parameters as all of these previous results for separable states or as some of the previous results for quantum correlations in some cases we can make use of the framework of lee raghavendra steurer lrs to establish integrality gaps for any sdp extended formulation not only the sos hierarchy our hardness result on separable states also yields a dimension lower bound of approximate disentanglers answering a question of watrous and aaronson et al these results can be viewed as limitations on the monogamy principle the ppt test the ability of tsirelson type bounds to restrict quantum correlations as well as the sdp hierarchies of doherty parrilo spedalieri navascues pironio acin and berta fawzi scholz indeed a wide range of past work in quantum information can be described as using an sdp on one of the above two problems and our results put broad limits on these lines of argument

metric and classical fidelity uncertainty relations for random unitary matrices we analyze uncertainty relations on finite dimensional hilbert spaces expressed in terms of classical fidelity which are stronger than metric uncertainty relations introduced by fawzi hayden and sen we establish the validity of fidelity uncertainty relations for random unitary matrices with optimal parameters up to universal constants which improves upon known results for the weaker notion of metric uncertainty this result is then applied to locking classical information in quantum states and allows to obtain optimal locking in hellinger distance improving upon previous results on locking in the total variation distance both by strengthening the metric used and by improving the dependence on parameters we also show that general probabilistic estimates behind the main theorem can be used to prove existence of data hiding schemes with bayesian type guarantees as a byproduct of our approach we obtain existence of almost euclidean subspaces of the matrix spaces with a better dimension distortion dependence than allowed in previously known constructions

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

local indistinguishability more nonlocality with less entanglement we provide a first operational method for checking local indistinguishability of orthogonal states it originates from that in ghosh et al phys rev lett 87 5807 2001 though we deal with pure states our method shows that probabilistic local distinguishing is possible for a complete multipartite orthogonal basis if and only if all vectors are product also it leads to local indistinguishability of a set of orthogonal pure states of 3 multiply sign in circle 3 which shows that one can have more nonlocality with less entanglement where more nonlocality is in the sense of increased local indistinguishability of orthogonal states this is to our knowledge the only known example where d orthogonal states in d multiply sign in circle d are locally indistinguishable

generalized schmidt decomposition and classification of three quantum bit states we prove for any pure three quantum bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form this leads to a canonical form which generalizes the two quantum bit schmidt decomposition it is uniquely characterized by the five entanglement parameters it leads to a complete classification of the three quantum bit states it shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties

interpolatability distinguishes locc from separable von neumann measurements local operations with classical communication locc and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement separable operations are strictly more powerful than locc but no simple explanation of this phenomenon is known we show that in the case of von neumann measurements the ability to interpolate measurements is an operational principle that sets apart locc and separable operations

critical behavior of a one dimensional fixed energy stochastic sandpile we study a one dimensional fixed energy version that is with no input or loss of particles of manna s stochastic sandpile model the system has a continuous transition to an absorbing state at a critical value of the particle density and exhibits the hallmarks of an absorbing state phase transition including finite size scaling critical exponents are obtained from extensive simulations which treat stationary and transient properties and an associated interface representation these exponents characterize the universality class of an absorbing state phase transition with a static conserved density in one dimension they differ from those expected at a linear interface depinning transition in a medium with point disorder and from those of directed percolation

limitations on separable measurements by convex optimization we prove limitations on locc and separable measurements in bipartite state discrimination problems using techniques from convex optimization specific results that we prove include an exact formula for the optimal probability of correctly discriminating any set of either three or four bell states via locc or separable measurements when the parties are given an ancillary partially entangled pair of qubits an easily checkable characterization of when an unextendable product set is perfectly discriminated by separable measurements along with the first known example of an unextendable product set that cannot be perfectly discriminated by separable measurements and an optimal bound on the success probability for any locc or separable measurement for the recently proposed state discrimination problem of yu duan and ying

how to efficiently select an arbitrary clifford group element we give an algorithm which produces a unique element of the clifford group on n qubits cn from an integer 0 i cn the number of elements in the group the algorithm involves o n 3 operations and provides in addition to a canonical mapping from the integers to group elements g a factorization of g into a sequence of at most 4n symplectic transvections the algorithm can be used to efficiently select random elements of cn which are often useful in quantum information theory and quantum computation we also give an algorithm for the inverse map indexing a group element in time o n 3

unifying typical entanglement and coin tossing on randomization in probabilistic theories it is well known that pure quantum states are typically almost maximally entangled and thus have close to maximally mixed subsystems we consider whether this is true for probabilistic theories more generally and not just for quantum theory we derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well defined it applies to typical entanglement in pure quantum states coin tossing in classical probability theory and randomization in post quantum theories a simple generalization yields the typical entanglement in anti symmetric quantum subspaces the formula is exact and simple only containing the number of degrees of freedom and the information capacity of the respective systems it allows us to generalize statistical physics arguments in a way which depends only on coarse properties of the underlying theory the proof of the formula generalizes several randomization notions to general probabilistic theories this includes a generalization of purity contributing to the recent effort of finding appropriate generalized entropy measures

universality split in absorbing phase transition with conserved field on fractal lattices the universality split in absorbing phase transition between the conserved lattice gas clg model and the conserved threshold transfer process cttp is investigated on a checkerboard fractal and on a sierpinski gasket the critical exponents theta beta nu and z which are associated with respectively the density of active particles in time the order parameter the temporal correlation length and the dynamics of active particles are elaborately measured for two models on selected fractal lattices the exponents for the clg model are found to be distinctly different from those of the cttp model on a checkerboard fractal whereas the two models exhibit the same critical behavior on a sierpinski gasket indicating that the universality split between the two models occurs only on a checkerboard fractal such a universality split is attributed from the dominant hopping mechanisms caused by the intrinsic properties of the underlying fractal lattice

entanglement cost of two qubit orthogonal measurements the entanglement cost of a bipartite measurement is the amount of shared entanglement two participants need to use up in order to carry out the given measurement by means of local operations and classical communication we numerically investigate the entanglement cost of generic orthogonal measurements on two qubits our results strongly suggest that for almost all measurements of this kind the entanglement cost is strictly greater than the average entanglement of the eigenstates associated with the measurements implying that the nonseparability of a two qubit orthogonal measurement is generically distinct from the nonseparability of its eigenstates

quantum key distribution based on orthogonal states allows secure quantum bit commitment for more than a decade it was believed that unconditionally secure quantum bit commitment qbc is impossible but based on a previously proposed quantum key distribution scheme using orthogonal states here we build a qbc protocol in which the density matrices of the quantum states encoding the commitment do not satisfy a crucial condition on which the no go proofs of qbc are based thus the no go proofs could be evaded our protocol is fault tolerant and very feasible with currently available technology it reopens the venue for other post cold war multi party cryptographic protocols e g quantum bit string commitment and quantum strong coin tossing with an arbitrarily small bias this result also has a strong influence on the clifton bub halvorson theorem which suggests that quantum theory could be characterized in terms of information theoretic constraints

the conditional common information in classical and quantum secret key distillation in this paper we consider two extensions of the gacs korner common information to three variables the conditional common information cci and the coarse grained conditional common information ccci both quantities are shown to be useful technical tools in the study of classical and quantum resource transformations in particular the ccci is shown to have an operational interpretation as the optimal rate of secret key extraction from an eavesdropped classical source p xyz when alice x and bob y are unable to communicate but share common randomness with the eavesdropper eve z moving to the quantum setting we consider two different ways of generating a tripartite quantum state from classical correlations p xyz 1 coherent encodings sum xyz sqrt p xyz xyz rangle and 2 incoherent encodings sum xyz p xyz xyz rangle langle xyz we study how well can alice and bob extract secret key from these quantum sources using quantum operations compared with the extraction of key from the underlying classical sources p xyz using classical operations while the power of quantum mechanics increases alice and bob s ability to generate shared randomness it also equips eve with a greater arsenal of eavesdropping attacks therefore it is not obvious who gains the greatest advantage for distilling secret key when replacing a classical source with a quantum one we first demonstrate that the classical key rate of p xyz is equivalent to the quantum key rate for an incoherent quantum encoding of the distribution for coherent encodings we next show that the classical and quantum rates are generally incomparable and in fact their difference can be arbitrarily large in either direction finally we introduce a zoo of entangled tripartite states all characterized by the conditional common information of their encoded probability distributions remarkably for these states almost all entanglement measures such as alice and bob s entanglement cost squashed entanglement and relative entropy of entanglement can be sharply bounded or even exactly expressed in terms of the conditional common information in the latter case we thus present a rare instance in which the various entropic entanglement measures of a quantum state can be explicitly calculated

distinguishability and indistinguishability by local operations and classical communication it is well known that orthogonal quantum states can be distinguished perfectly however if we assume that these orthogonal quantum states are shared by spatially separated parties the distinguishability of these shared quantum states may be completely different we show that a set of linearly independent quantum states formula see text where u m n are generalized pauli matrices cannot be discriminated deterministically or probabilistically by local operations and classical communication on the other hand any l maximally entangled states from this set are locally distinguishable if l l 1 or 2d the explicit projecting measurements are obtained to locally discriminate these states as an example we show that four werner states are locally indistinguishable

local random quantum circuits are approximate polynomial designs numerical results we numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbor two qubit gates form an approximate unitary poly n design brandao et al 2012 arxiv 1208 0692 using a group theory formalism spectral gaps that give a ratio of convergence to a given t design are evaluated for a different number of qubits n up to 20 and degrees t t 2 3 4 and 5 improving previously known results for n 2 in the case of t 2 and 3 their values lead to the conclusion that the previously used lower bound that bounds spectral gaps values may give very little information about the real situation and in most cases only tells us that a gap is closed we compare our results to another lower bounding technique again showing that its results may not be tight

local distinguishability of any three quantum states we prove that any three linearly independent pure quantum states can always be locally distinguished with nonzero probability regardless of their dimension entanglement or multipartite structure almost always all three states can be unambiguously identified the only exceptional case where one state is locally knowable but the other two are not is found among multi qubit states

mean value theorems of multiplicative functions on additive arithmetic semigroups it has been pointed out to me by r warlimont that the proof of theorem 6 4 2 in 1 has a gap and the theorem is false he has also constructed counter examples in accordance theorem 1 6 in my paper 2 quoted in the title of this correction is false too actually either of them requires more conditions on the multiplicative functions so that it can be true in this correction we supply such a condition see condition 2 below and prove the following theorem theorem suppose an additive arithmetic semigroupg satisfies the condition i or ii in theorem 1 6 in 2 let f a be a multiplicative function such that f a 1 for every a g if there exist a subset p1 of p and a constant 0 such that p p1 q p

active absorbing state phase transition beyond directed percolation a class of exactly solvable models we introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active absorbing state phase transition at finite density in this model an occupied site is defined to be active if its left neighbor is occupied and the right neighbor is vacant particles from such active sites hop stochastically to their right we show that both the density of active sites and the survival probability vanish as the particle density is decreased below half the critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz exact analytical study of several variations of the model reveals that these nonequilibrium phase transitions belong to a new universality class different from the generic active absorbing state phase transition namely directed percolation

distinguishing multi partite states by local measurements we analyze the distinguishability norm on the states of a multi partite system defined by local measurements concretely we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent to a multi partite generalisation of the non commutative ell 2 norm aka hilbert schmidt norm in comparing the two the constants of domination depend only on the number of parties but not on the hilbert spaces dimensions

vector representations of graphs and distinguishing quantum product states with one way locc abstract distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory we introduce a graph theoretic approach based on the theory of vector representations of graphs to the core problem of distinguishing product states with one way locc we establish a number of results that show how distinguishing such states can be framed in terms of properties of the underlying graphs associated with a set of vector product states we also present a number of illustrative examples

composite parameterization and haar measure for all unitary and special unitary groups we adopt the concept of the composite parameterization of the unitary group u d to the special unitary group su d furthermore we also consider the haar measure in terms of the introduced parameters we show that the well defined structure of the parameterization leads to a concise formula for the normalized haar measure on u d and su d with regard to possible applications of our results we consider the computation of high order integrals over unitary groups

rank two bipartite bound entangled states do not exist we explore the relation between the rank of a bipartite density matrix and the existence of bound entanglement we show a relation between the rank marginal ranks and distillability of a mixed state and use this to prove that any rank n bound entangled state must have support on no more than an n n hilbert space a direct consequence of this result is that there are no bipartite bound entangled states of rank two we also show that a separability condition in terms of a quantum entropy inequality is associated with the above results we explore the idea of how many pure states are needed in a mixture to cancel the distillable entanglement of a schmidt rank n pure state and provide a lower bound of n 1 we also prove that a mixture of a non zero amount of any pure entangled state with a pure product state is distillable

comment on random quantum circuits are approximate 2 designs by a w harrow and r a low commun math phys 291 257 302 2009 in a w harrow and r a low commun math phys 291 1 257 302 2009 it was shown that a quantum circuit composed of random 2 qubit gates converges to an approximate quantum 2 design in polynomial time we point out and correct a flaw in one of the paper s main arguments our alternative argument highlights the role played by transpositions induced by the random gates in achieving convergence

four locally indistinguishable ququad ququad orthogonal maximally entangled states we explicitly exhibit a set of four ququad ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication before our work it was unknown whether there is a set of d locally indistinguishable d d orthogonal maximally entangled states for some positive integer d we further show that a 2 2 maximally entangled state can be used to locally distinguish this set of states without being consumed thus demonstrate a novel phenomenon of entanglement discrimination catalysis based on this set of states we construct a new set k consisting of four locally indistinguishable states such that k m with 4 m members is locally distinguishable for some m greater than one as an immediate application we construct a noisy quantum channel with one sender and two receivers whose local zero error classical capacity can achieve the full dimension of the input space but only with a multi shot protocol

distinguishability of quantum states by separable operations in this paper we study the distinguishability of multipartite quantum states by separable operations we first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations an analytical version of this condition is derived for the case of d 1 pure states where d is the total dimension of the state space under consideration a number of interesting consequences of this result are then carefully investigated remarkably we show there exists a large class of 2 otimes 2 separable operations not being realizable by local operations and classical communication before our work only a class of 3 otimes 3 nonlocal separable operations was known bennett phys rev a 59 1070 1999 we also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of one or two orthogonal product states i e has an orthogonal schmidt number not less than three thus generalize the recent work about indistinguishable bipartite subspaces watrous phys rev lett 95 080505 2005 notably we obtain an explicit construction of indistinguishable subspaces of dimension 7 or 6 by considering a composite quantum system consisting of two qutrits resp three qubits which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8

a sufficient and necessary condition for 2n 1 orthogonal states to be locally distinguishable in a c2 cn system we investigate the local distinguishability of a set of orthogonal states on c2 cn by mathematical induction we prove that a set of 2n 1 orthogonal states on c2 cn can be locally discriminated by local operation and classical communication if and only if at most one of them is entangled that is the sum of schmidt rank of these states should be no greater than the total hilbert space dimension 2n furthermore we give some discussion about locally distinguishing any number of orthogonal states on c2 cn and explain why this schmidt rank criterion cannot be generalized to locally discriminate any number of orthogonal states

unextendible product bases uncompletable product bases and bound entanglement we report new results and generalizations of our work on unextendible product bases upb uncompletable product bases and bound entanglement we present a new construction for bound entangled states based on product bases which are only completable in a locally extended hilbert space we introduce a very useful representation of a product basis an orthogonality graph using this representation we give a complete characterization of unextendible product bases for two qutrits we present several generalizations of upbs to arbitrary high dimensions and multipartite systems we present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators we prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement

distinguishability of bell states more than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication locc are allowed we show that four bell states cannot be discriminated by locc even probabilistically using the separability properties of a four party unlockable bound entangled state using an existing inequality among the measures of entanglement we show that any three bell states cannot be discriminated with certainty by locc exploiting the inequality we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states

on the explicit constructions of certain unitary t designs unitary t designs are good finite subsets of the unitary group ug d that approximate the whole unitary group ug d well unitary t designs have been applied in randomized benchmarking tomography quantum cryptography and many other areas of quantum information science if a unitary t design itself is a group then it is called a unitary t group although it is known that unitary t designs in ug d exist for any t and d the unitary t groups do not exist for t geq 4 if d geq 3 as it is shown by guralnick tiep 2005 and bannai navarro rizo tiep bnrt 2018 explicit constructions of exact unitary t designs in ug d are not easy in general in particular explicit constructions of unitary 4 designs in ug 4 have been an open problem in quantum information theory we prove that some exact unitary t 1 designs in the unitary group ug d are constructed from unitary t groups in ug d that satisfy certain specific conditions based on this result we specifically construct exact unitary 3 designs in ug 3 from the unitary 2 group sl 3 2 in ug 3 and also unitary 4 designs in ug 4 from the unitary 3 group sp 4 3 in ug 4 numerically we also discuss some related problems and a few applications to physics problems

hilbert s projective metric in quantum information theory we introduce and apply hilbert s projective metric in the context of quantum information theory the metric is induced by convex cones such as the sets of positive separable or positive partial transpose operators it provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under protocols involving local quantum operations and classical communication or under other cone preserving operations the results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels for instance improving ruskai s trace norm contraction inequality a new duality between distinguishability measures and base norms is provided for two given pairs of quantum states we show that the contraction of hilbert s projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other inequalities between hilbert s projective metric and the chernoff bound the

elementary proofs of the abstract prime number theorem for algebraic function fields elementary proofs of the abstract prime number theorem of the form m q m o q m m 751 for algebraic function fields are given the proofs use a refinement of a tauberian theorem of bombieri

distinguishing bipartitite orthogonal states using locc best and worst cases two types of results are presented for distinguishing pure bipartite quantum states using local operations and classical communications we examine sets of states that can be perfectly distinguished in particular showing that any three orthogonal maximally entangled states in c3 c3 form such a set in cases where orthogonal states cannot be distinguished we obtain upper bounds for the probability of error using locc taken over all sets of k orthogonal states in cn cm in the process of proving these bounds we identify some sets of orthogonal states for which perfect distinguishability is not possible

scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension we analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field phys rev lett 85 1803 2000 we determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in d 2 3 4 5 dimensions a comparison of our results and those obtained from a mean field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four

testing for a pure state with local operations and classical communication we examine the problem of using local operations and classical communication locc to distinguish a known pure state from an unknown possibly mixed state bounding the error probability from above and below we study the asymptotic rate of detecting multiple copies of the pure state and show that if the overlap of the two states is great enough then they can be distinguished asymptotically as well with locc as with global measurements otherwise the maximal schmidt coefficient of the pure state is sufficient to determine the asymptotic error rate

enhancing the security of quantum communication by hiding the message in a superposition a new method to hide specific quantum states in a superposition will be proposed the proposed method is used to hide an encrypted message in a superposition the process of hiding and unhiding the target quantum states is fast by using a single iteration of the amplitude amplification operators this makes the message 100 safe by direct measurement from an eavesdropper no entanglement sharing is required among the communicating parties

generic local distinguishability and completely entangled subspaces a subspace of a multipartite hilbert space is completely entangled if it contains no product states such subspaces can be large with a known maximum size smax approaching the full dimension of the system d we show that almost all subspaces with dimension s smax are completely entangled and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n d smax this condition holds for almost all sets of states of all multipartite systems and reveals something surprising the criterion is identical for separable and nonseparable states entanglement makes no difference

mutually unbiased bases generalized spin matrices and separability abstract a collection of orthonormal bases for a complex d dimensional hilbert space is called mutually unbiased mub if for any two vectors v and w from different bases the square of the inner product equals 1 d v w 2 1 d the mub problem is to prove or disprove the existence of a maximal set of d 1 bases it has been shown in ann phys 191 1989 363 that such a collection exists if d is a power of a prime number p we revisit this problem and use d d generalizations of the pauli spin matrices to give a constructive proof of this result specifically we give explicit representations of commuting families of unitary matrices whose eigenvectors solve the mub problem additionally we give formulas from which the orthogonal bases can be readily computed we show how the techniques developed here provide a natural way to analyze the separability of the bases the techniques used require properties of algebraic field extensions and the relevant part of that theory is included in the appendix

on the chernoff distance for asymptotic locc discrimination of bipartite quantum states motivated by the recent discovery of a quantum chernoff theorem for asymptotic state discrimination we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication locc in the limit of many copies while for two pure states a result of walgate et al shows that locc is just as powerful as global measurements data hiding states divincenzo et al show that locality can impose severe restrictions on the distinguishability of even orthogonal states here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states extremal d d werner states by a linear programming approach surprisingly the single copy optimal measurement remains optimal for n copies in the sense that the best strategy is measuring each copy separately followed by a simple classical decision rule we also put a lower bound on the bias with which states can be distinguished by separable operations

everything you always wanted to know about locc but were afraid to ask in this paper we study the subset of generalized quantum measurements on finite dimensional systems known as local operations and classical communication locc while locc emerges as the natural class of operations in many important quantum information tasks its mathematical structure is complex and difficult to characterize here we provide a precise description of locc and related operational classes in terms of quantum instruments our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds while the set of locc is not topologically closed we show that finite round locc constitutes a compact subset of quantum operations additionally we show the existence of an open ball around the completely depolarizing map that consists entirely of locc implementable maps finally we demonstrate a two qubit map whose action can be approached arbitrarily close using locc but nevertheless cannot be implemented perfectly

separability problem for multipartite states of rank at most 4 one of the most important problems in quantum information is the separability problem which asks whether a given quantum state is separable we investigate multipartite states of rank at most 4 which are ppt i e all their partial transposes are positive semidefinite we show that any ppt state of rank 2 or 3 is separable and has length at most 4 for separable states of rank 4 we show that they have length at most 6 it is six only for some qubit qutrit or multiqubit states it turns out that any ppt entangled state of rank 4 is necessarily supported on a 3 3 or a 2 2 2 subsystem we obtain a very simple criterion for the separability problem of the ppt states of rank at most 4 such a state is entangled if and only if its range contains no product vectors this criterion can be easily applied since a four dimensional subspace in the 3 3 or 2 2 2 system contains a product vector if and only if its plucker coordinates satisfy a homogeneous polynomial equation the chow form of the corresponding segre variety we have computed an explicit determinantal expression for the chow form in the former case while such an expression was already known in the latter case

the emergence of typical entanglement in two party random processes we investigate the entanglement within a system undergoing a random local process we find that there is initially a phase of very fast generation and spread of entanglement at the end of this phase the entanglement is typically maximal in oliveira et al 2007 phys rev lett 98 130502 we proved that the maximal entanglement is reached to a fixed arbitrary accuracy within o n3 steps where n is the total number of qubits here we provide a detailed and more pedagogical proof we demonstrate that one can use the so called stabilizer gates to simulate this process efficiently on a classical computer furthermore we discuss three ways of identifying the transition from the phase of rapid spread of entanglement to the stationary phase i the time when saturation of the maximal entanglement is achieved ii the cutoff moment when the entanglement probability distribution is practically stationary and iii the moment block entanglement exhibits volume scaling we furthermore investigate the mixed state and multipartite setting numerically we find that the mutual information appears to behave similarly to the quantum correlations and that there is a well behaved phase space flow of entanglement properties towards an equilibrium we describe how the emergence of typical entanglement can be used to create a much simpler tripartite entanglement description the results form a bridge between certain abstract results concerning typical also known as generic entanglement relative to an unbiased distribution on pure states and the more physical picture of distributions emerging from random local interactions

unextendible product bases and bound entanglement an unextendible product basis upb for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state we give examples of upbs and show that the uniform mixed state over the subspace complementary to any upb is a bound entangled state we exhibit a tripartite 2 3 2 3 2 upb whose complementary mixed state has tripartite entanglement but no bipartite entanglement i e all three corresponding 2 3 4 bipartite mixed states are unentangled we show that members of a upb are not perfectly distinguishable by local positive operator valued measurements and classical communication s0031 9007 99 09360 6

operator structures and quantum one way locc conditions we conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one way local operations and classical communications locc we show how operator structures such as operator systems operator algebras and hilbert c modules naturally arise in this setting we make use of these structures to derive new results and bounds in the study of one way locc and we use the approach to uncover new derivations of some previously established results

purity distribution for bipartite random pure states analytic expressions for the probability density distribution of the linear entropy and the purity are derived for bipartite pure random quantum states the explicit distributions for a state belonging to a product of hilbert spaces of dimensions p and q are given for p 3 and any q 3 as well as for p q 4

sandpiles with height restrictions we study stochastic sandpile models with a height restriction in one and two dimensions a site can topple if it has a height of two as in manna s model but in contrast to previously studied sandpiles here the height or number of particles per site cannot exceed two this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded two toppling rules are considered in one the particles are redistributed independently while the other involves some cooperativity we study the fixedenergy system no input or loss of particles using cluster approximations and extensive simulations and find that it exhibits a continuous phase transition to an absorbing state at a critical value z c of the particle density the critical exponents agree with those of the unrestricted manna sandpile