one shot coherence dilution manipulation and quantification of quantum resources are fundamental problems in quantum physics in the asymptotic limit coherence distillation and dilution have been proposed by manipulating infinite identical copies of states in the nonasymptotic setting finite data size effects emerge and the practically relevant problem of coherence manipulation using finite resources has been left open this letter establishes the one shot theory of coherence dilution which involves converting maximally coherent states into an arbitrary quantum state using maximally incoherent operations dephasing covariant incoherent operations incoherent operations or strictly incoherent operations we introduce several coherence monotones with concrete operational interpretations that estimate the one shot coherence cost the minimum amount of maximally coherent states needed for faithful coherence dilution furthermore we derive the asymptotic coherence dilution results with maximally incoherent operations incoherent operations and strictly incoherent operations as special cases our result can be applied in the analyses of quantum information processing tasks that exploit coherence as resources such as quantum key distribution and random number generation

presence of quantum correlations results in a nonvanishing ergotropic gap the paradigm of extracting work from an isolated quantum system through a cyclic hamiltonian process is a topic of immense research interest the optimal work extracted under such a process is termed ergotropy europhys lett 67 565 2004 here in a multiparty scenario we consider only a class of such cyclic processes that can be implemented locally giving rise to the concept of local ergotropy eventually the presence of quantum correlations results in a nonvanishing thermodynamic quantity called an ergotropic gap measured by the difference between global and local ergotropy however the converse does not hold in general i e its nonzero value does not necessarily imply the presence of quantum correlations for arbitrary multiparty states we quantify this gap we also evaluate the difference between maximum global and local extractable work for arbitrary states when the system is no longer isolated but put in contact with a bath of the same local temperature

a new method of constructing symmetry adapted linear combinations for a finite group ii correspondence theorem and basis operators abstract a correspondence theorem is introduced to describe the relation between an elementary basis function and a symmetry adapted linear combination belonging to the same irreducible representation of a point group by means of basis operators the general expressions are given for the symmetry adapted linear combinations the coupling coefficients the lattice harmonics and the hybrid atomic orbitals illustrative examples are discussed to demonstrate the effectiveness of the formalism

quantum work statistics and resource theories bridging the gap through renyi divergences the work performed on or extracted from a nonautonomous quantum system described by means of a two point projective measurement approach is a stochastic variable we show that the cumulant generating function of work can be recast in the form of quantum r enyi ensuremath alpha divergences and by exploiting the convexity of this cumulant generating function derive a single parameter family of bounds for the first moment of work higher order moments of work can also be obtained from this result in this way we establish a link between quantum work statistics in stochastic approaches and resource theories for quantum thermodynamics a theory in which r enyi ensuremath alpha divergences take a central role to explore this connection further we consider an extended framework involving a control switch and an auxiliary battery which is instrumental to reconstructing the work statistics of the system we compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource theoretic settings

relative submajorization and its use in quantum resource theories we introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics bipartite entanglement and quantum coherence relative majorization is an ordering on pairs of vectors induced by stochastic transformations one pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair in the context of resource theories we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another also when assisted by additional standard resources such as useful work or maximally entangled states these characterizations have a geometric formulation as the ratios or differences respectively between the lorenz curves associated with the input and output resources making them efficient to compute we also find several interesting bounds on the reversibility of a given transformation in terms of the properties of the forward transformation the main technical tool used to establish these results is the linear programming duality which is used to show that any instance of relative submajorization can be dilated to an instance of strict relative majorization we introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics bipartite entanglement and quantum coherence relative majorization is an ordering on pairs of vectors induced by stochastic transformations one pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair in the context of resource theories we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another also when assisted by additional standard resources such as useful work or maximally entangled states these characterizations have a geometric formulation as the ratios or differences respectively

the second laws of quantum thermodynamics the second law of thermodynamics places constraints on state transformations it applies to systems composed of many particles however we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath is there a second law of thermodynamics in this regime here we find that for processes which are approximately cyclic the second law for microscopic systems takes on a different form compared to the macroscopic scale imposing not just one constraint on state transformations but an entire family of constraints we find a family of free energies which generalize the traditional one and show that they can never increase the ordinary second law relates to one of these with the remainder imposing additional constraints on thermodynamic transitions we find three regimes which determine which family of second laws govern state transitions depending on how cyclic the process is in one regime one can cause an apparent violation of the usual second law through a process of embezzling work from a large system which remains arbitrarily close to its original state these second laws are relevant for small systems and also apply to individual macroscopic systems interacting via long range interactions by making precise the definition of thermal operations the laws of thermodynamics are unified in this framework with the first law defining the class of operations the zeroth law emerging as an equivalence relation between thermal states and the remaining laws being monotonicity of our generalized free energies

a resource framework for quantum shannon theory quantum shannon theory is loosely defined as a collection of coding theorems such as classical and quantum source compression noisy channel coding theorems entanglement distillation etc which characterize asymptotic properties of quantum and classical channels and states in this paper we advocate a unified approach to an important class of problems in quantum shannon theory consisting of those that are bipartite unidirectional and memoryless

a generalization of majorization that characterizes shannon entropy we introduce a binary relation on the finite discrete probability distributions which generalizes notions of majorization that have been studied in quantum information theory motivated by questions in thermodynamics our relation describes the transitions induced by bistochastic maps in the presence of additional auxiliary systems which may become correlated in the process we show that this relation is completely characterized by shannon entropy h which yields an interpretation of h in resource theoretic terms and admits a particularly simple proof of a known characterization of h in terms of natural information theoretic properties

α z renyi relative entropies we consider a two parameter family of renyi relative entropies d z that are quantum generalisations of the classical renyi divergence d p q this family includes many known relative entropies or divergences such as the quantum relative entropy the recently defined quantum renyi divergences as well as the quantum renyi relative entropies all its members satisfy the quantum generalizations of renyi s axioms for a divergence we consider the range of the parameters z for which the data processing inequality holds we also investigate a variety of limiting cases for the two parameters obtaining explicit formulas for each one of them

rigidity of asymptotically conical shrinking gradient ricci solitons we show that if two gradient shrinking ricci solitons are asymptotic along some end of each to the same regular cone 0 dr rg then the soliton metrics must be isometric on some neighborhoods of infinity of these ends our theorem imposes no restrictions on the behavior of the metrics off of the ends in question and in particular does not require their geodesic completeness as an application we prove that the only complete connected gradient shrinking ricci soliton asymptotic to a rotationally symmetric cone is the gaussian soliton on r

catalytic transformations for bipartite pure states entanglement catalysis is a phenomenon that usually enhances the conversion probability in the transformation of entangled states by the temporary involvement of another entangled state so called catalyst where after the process is completed the catalyst is returned to the same state for some pairs of bipartite pure entangled states catalysis enables a transformation with unit probability of success in which case the respective schmidt coefficients of the states are said to satisfy the trumping relation a mathematical relation which is an extension of the majorization relation this paper provides all necessary and sufficient conditions for the trumping and two other associated relations using these conditions the least upper bound of conversion probabilities using catalysis is also obtained moreover best conversion ratios achievable with catalysis are found for transformations involving many copies of states

area minimizing projective planes in 3 manifolds let m g be a compact riemannian manifold of dimension 3 and let denote the collection of all embedded surfaces homeomorphic to input amssym bbb r bbb p 2 we study the infimum of the areas of all surfaces in this quantity is related to the systole of m g it makes sense whenever is nonempty in this paper we give an upper bound for this quantity in terms of the minimum of the scalar curvature of m g moreover we show that equality holds if and only if m g is isometric to input amssym bbb r bbb p 3 up to scaling the proof uses the formula for the second variation of area and hamilton s ricci flow 2010 wiley periodicals inc

passivity complete passivity and virtual temperatures we give a simple and intuitive proof that the only states which are completely passive i e those states from which work cannot be extracted even with infinitely many copies are gibbs states at positive temperatures the proof makes use of the idea of virtual temperatures i e the association of temperatures to pairs of energy levels transitions we show that 1 passive states are those where every transition is at a positive temperature and 2 completely passive states are those where every transition is at the same positive temperature

self catalytic conversion of pure quantum states conversion of entangled states under stochastic local operations and classical communication s locc admits the phenomenon of catalysis here we explore the possibility of a copy of the initial state itself performing as a catalyst which we call a self catalytic process we show explicit examples of self catalysis necessary and sufficient conditions for the phenomenon to take place are discussed we numerically estimate how frequent it is and we show that increasing the number of copies used as catalyst can increase the probability of conversion but does not make the process deterministic by the end we conjecture that under locc the probability of finding a self catalytic reaction does not increase monotonically with the dimensions whereas under slocc it does increase

average coherence and its typicality for random mixed quantum states the wishart ensemble is a useful and important random matrix model used in diverse fields by realizing induced random mixed quantum states as a wishart ensemble with fixed unit trace using matrix integral technique we give a fast track to the average coherence for random mixed quantum states induced via partial tracing of the haar distributed bipartite pure states as a direct consequence of this result we get a compact formula for the average subentropy of random mixed states these compact formulae extend our previous work

efficiency versus speed in quantum heat engines rigorous constraint from lieb robinson bound a long standing open problem whether a heat engine with finite power achieves the carnot efficiency is investgated we rigorously prove a general trade off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines in a first step employing the lieb robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable this inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished using this description we prove an upper bound on efficiency with the aid of quantum information geometry our result generally excludes the possibility of a process with finite speed at the carnot efficiency in quantum heat engines in particular the obtained constraint covers engines evolving with non markovian dynamics which almost all previous studies on this topic fail to address

the minimum entropy output of a quantum channel is locally additive we show that the minimum von neumann entropy output of a quantum channel is locally additive hastings counterexample for the additivity conjecture makes this result quite surprising in particular it indicates that the nonadditivity of the minimum entropy output is a global effect of quantum channels

a unified theory of point groups vi the projective corepresentations of the magnetic point groups of infinite order this paper provides all the p inequivalent projective irreducible unitary corepresentations of all the magnetic point groups of infinite order with full use of their isomorphisms

manifolds with positive curvature operators are space forms the ricci flow was introduced by hamilton in 1982 h1 in order to prove that a compact three manifold admitting a riemannian metric of positive ricci curvature is a spherical space form in dimension four hamilton showed that compact four manifolds with positive curvature operators are spherical space forms as well h2 more generally the same conclusion holds for compact four manifolds with 2 positive curvature operators che recall that a curvature operator is called 2 positive if the sum of its two smallest eigenvalues is positive in arbitrary dimensions huisken hu described an explicit open cone in the space of curvature operators such that the normalized ricci flow evolves metrics whose curvature operators are contained in that cone into metrics of constant positive sectional curvature hamilton conjectured that in all dimensions compact riemannian manifolds with positive curvature operators must be space forms in this paper we confirm this conjecture more generally we show the following

on wilking s criterion for the ricci flow wilking has recently shown that one can associate a ricci flow invariant cone of curvature operators c s which are nonnegative in a suitable sense to every ad so n mathbb c invariant subset s subset mathbf so n mathbb c in this article we show that if s is an ad so n mathbb c invariant subset of mathbf so n mathbb c such that s cup 0 is closed and c s subset c s denotes the cone of curvature operators which are positive in the appropriate sense then one of the two possibilities holds a the connected sum of any two riemannian manifolds with curvature operators in c s also admits a metric with curvature operator in c s b the normalized ricci flow on any compact riemannian manifold m with curvature operator in c s converges to a metric of constant positive sectional curvature we also point out that if s is an arbitrary ad so n mathbb c subset then c s is contained in the cone of curvature operators with nonnegative isotropic curvature

on quantum renyi entropies a new generalization and some properties the renyi entropies constitute a family of information measures that generalizes the well known shannon entropy inheriting many of its properties they appear in the form of unconditional and conditional entropies relative entropies or mutual information and have found many applications in information theory and beyond various generalizations of renyi entropies to the quantum setting have been proposed most prominently petz s quasi entropies and renner s conditional min max and collision entropy however these quantum extensions are incompatible and thus unsatisfactory we propose a new quantum generalization of the family of renyi entropies that contains the von neumann entropy min entropy collision entropy and the max entropy as special cases thus encompassing most quantum entropies in use today we show several natural properties for this definition including data processing inequalities a duality relation and an entropic uncertainty relation

maximum one shot dissipated work from renyi divergences thermodynamics describes large scale slowly evolving systems two modern approaches generalize thermodynamics fluctuation theorems which concern finite time nonequilibrium processes and one shot statistical mechanics which concerns small scales and finite numbers of trials combining these approaches we calculate a one shot analog of the average dissipated work defined in fluctuation contexts the cost of performing a protocol in finite time instead of quasistatically the average dissipated work has been shown to be proportional to a relative entropy between phase space densities to a relative entropy between quantum states and to a relative entropy between probability distributions over possible values of work we derive one shot analogs of all three equations demonstrating that the order infinity renyi divergence is proportional to the maximum possible dissipated work in each case these one shot analogs of fluctuation theorem results contribute to the unification of these two toolkits for small scale nonequilibrium statistical physics

extremal distributions under approximate majorization although an input distribution may not majorize a target distribution it may majorize a distribution which is close to the target here we consider a notion of approximate majorization for any distribution and given a distance we find the approximate distributions which majorize are majorized by all other distributions within the distance we call these the steepest and flattest approximation this enables one to compute how close one can get to a given target distribution under a process governed by majorization we show that the flattest and steepest approximations preserve ordering under majorization furthermore we give a notion of majorization distance this has applications ranging from thermodynamics entanglement theory and economics

work fluctuation dissipation trade off in heat engines reducing work fluctuation and dissipation in heat engines or more generally information heat engines that perform feedback control is vital to maximize their efficiency the same problem arises when we attempt to maximize the efficiency of a given thermodynamic task that undergoes nonequilibrium processes for arbitrary initial and final states we find that the most general trade off relation between work fluctuation and dissipation applicable to arbitrary nonequilibrium processes is bounded from below by the information distance characterizing how far the system is from thermal equilibrium the minimum amount of dissipation is found to be given in terms of the relative entropy and the renyi divergence both of which quantify the information distance between the state of the system and the canonical distribution we give an explicit protocol that achieves the fundamental lower bound of the trade off relation

the 32 minimal general generator sets of 230 double space groups the 32 minimal general generator sets mggs for the three dimensional double space groups are provided each mggs has a very limited number of parameters that describe the translational parts of the space groups belonging to a crystal class the method of construction is based on the algebraic defining relations of the abstract generators of the point groups the equivalence or inequivalence criteria for the space groups with respect to lattice transformations are established by introducing the definite set u of the unimodular matrices that leaves a lattice type l of each crystal class g based on the set u it will be shown that mere shifts of the lattice origin are necessary and sufficient to determine the inequivalence of almost all the space groups belonging to a crystal class of high symmetry it is simpler to construct mggs of higher symmetry than those of lower symmetry this contrasts with the existing methods which are based on the solvability of the space groups

a unified theory of the point groups iii classification and basis functions of improper point groups this paper introduces a new system of classification of improper point groups which is most effective for describing their general irreducible representations the complete set of the general angular momentum eigenfunctions is classified according to the general irreducible representations of the seven sets of the improper point groups corresponding to cn c and dn d for an aribtrary n

minimal two spheres and the topology of manifolds with positive curvature on totally isotropic two planes there has been much interest among differential geometers in finding relationships between curvature and topology of riemannian manifolds for the most part efforts have been directed towards understanding the implications of positive or negative sectional curvature ricci curvature or scalar curvature but there are other hypotheses on the curvature which also deserve investigation in this article we will consider the topological implications of a new curvature assumption positive curvature on totally isotropic two planes and we will prove via the sacks uhlenbeck theory of minimal two spheres that a compact simply connected riemannian manifold of dimension at least four with positive curvature on totally isotropic two planes is homeomorphic to a sphere as corollaries we will obtain a proof via minimal two spheres for riemannian manifolds of dimension at least four of the berger klingenberg rauch toponogov sphere theorem strengthened to pointwise quarter pinching as well as a proof that every simply connected compact riemannian manifold with positive curvature operators is homeomorphic to a sphere let m be an n dimensional riemannian manifold with tangent space tpm at the point p e m recall that the curvature operator at p is the self adjoint

a unified theory of the point groups iv the general corepresentations of the crystallographic and noncrystallographic shubnikov point groups a new system of classification for all the shubnikov point groups gs is presented which is best suited for describing their isomorphisms as well as their construction by the new classification and the modified form of the corepresentations there are presented the simple general expressions of the irreducible corepresentations for the 10 minimum sets of proper gs from which all coirreps of the remaining gs follow icosahedral groups are excluded

general irreducibility condition for vector and projective corepresentations of antiunitary groups a general condition for irreducibility of vector and projective corepresentations of an antiunitary group is presented it depends only on the characters of the unitary halving subgroup of the covering group it reduces to the well known type criterion of corepresentations when it is specialized to the three types of corepresentations

a lie algebraic approach to ricci flow invariant curvature conditions and harnack inequalities we consider a subset s of the complex lie algebra so n c and the cone c s of curvature operators which are nonnegative on s we show that c s defines a ricci flow invariant curvature condition if s is invariant under adso n c the analogue for kahler curvature operators holds as well although the proof is very simple and short it recovers all previously known invariant nonnegativity conditions as an application we reprove that a compact kahler manifold with positive orthogonal bisectional curvature evolves to a manifold with positive bisectional curvature and is thus biholomorphic to cp moreover the methods can also be applied to prove harnack inequalities we consider a lie algebra g endowed with a scalar product which is invariant under the adjoint representation of the lie algebra the reader should think of g either as the space so n of skew adjoint endomorphism of r with the scalar product a b 1 2 tr ab or of the lie subalgebra u n so 2n corresponding to the unitary group u n so 2n endowed with the induced scalar product we consider the space of selfadjoint endomorphisms of s g every selfadjoint endomorphism r s g is determined by the corresponding bilinear form x y 7 rx y the extension of this form to a complex bilinear form r g r c g r c c will be denoted with the same letter r notice that for any x g r c the number r x x is real where x 7 x is complex conjugation also recall that the space of algebraic curvature operators s b so n is a linear subspace of s so n similarly the space of algebraic kahler curvature operators s k u n is a linear subspace of s u n the subspaces are also invariant under the ricci flow ode on s g r r r where rx y 12 tr adx r ady r for x y g we have the following basic result theorem 1 let s be a subset of the complex lie algebra g r c and let gc denote a lie group with lie algebra g r c if s is invariant under the adjoint representation of gc then for h r the set c s h r s g r v v h for all v s is invariant under the ode r r r in many cases s is scaling invariant and then h 0 is the only meaningful choice for h 0 the set c s c s 0 is a cone and the curvature condition c s can be thought of as a nonnegativity condition we recall that for a o n invariant subset c s so n we say that a manifold satisfies c if the curvature operator

optimal performance of generalized heat engines with finite size baths of arbitrary multiple conserved quantities beyond independent and identical distribution scaling in quantum thermodynamics effects of finiteness of the baths have been less considered in particular there is no general theory which focuses on finiteness of the baths of multiple conserved quantities then we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths in the context of general theories of quantum thermodynamics the size of the baths has been given in terms of the number of identical copies of a system which does not cover even such a natural scaling as the volume in consideration of the asymptotic extensivity we deal with a generic scaling of the baths to naturally include the volume scaling based on it we derive a bound for the performance of generalized heat engines reflecting finite size effects of the baths which we call fine grained generalized carnot bound we also construct a protocol to achieve the optimal performance of the engine given by this bound finally applying the obtained general theory we deal with simple examples of generalized heat engines as for an example of non independent and identical distribution scaling and multiple conserved quantities we investigate a heat engine with two baths composed of an ideal gas exchanging particles where the volume scaling is applied the result implies that the mass of the particle explicitly affects the performance of this engine with finite size baths

a limit of the quantum renyi divergence recently an interesting quantity called the quantum renyi divergence or sandwiched renyi relative entropy was defined for pairs of positive semi definite operators and it depends on a parameter and acts as a parent quantity for other relative entropies which have important operational significance in quantum information theory the quantum relative entropy and the min and max relative entropies there is however another relative entropy called the 0 relative renyi entropy which plays a key role in the analysis of various quantum information processing tasks in the one shot setting we prove that the 0 relative renyi entropy is obtainable from the quantum renyi divergence only if and have equal supports this along with existing results in the literature suggests that it suffices to consider two essential parent quantities from which operationally relevant entropic quantities can be derived the quantum renyi divergence with parameter 1 2 and the relative renyi entropy with 0 1

an entropic analysis of approximate quantum error correction abstract the concept of entropy and the correct application of the second law of thermodynamics are essential in order to understand the reason why quantum error correction is thermodynamically possible and no violation of the second law occurs during its execution we report in this work our first steps towards an entropic analysis extended to approximate quantum error correction qec special emphasis is devoted to the link among quantum state discrimination qsd quantum information gain and quantum error correction in both the exact and approximate qec scenarios

a unified theory of the point groups v the general projective corepresentations of the magnetic point groups and their applications to magnetic space groups this paper presents the general expressions of the projective irreducible corepresentations of the 20 homologous sets of the magnetic double point groups from which follow all those of the remaining groups of finite order through isomorphisms the icosahedral group is excluded these are explicitly given in terms of the irreducible representations of the unitary double point groups their special cases provide all the irreducible corepresentations of all magnetic space groups of wave vector through simple gauge transformations a method of determining the gauge transformations is discussed through typical examples

rigidity of einstein manifolds with positive scalar curvature we prove that if m n n ge 4 is a compact einstein manifold whose normalized scalar curvature and sectional curvature satisfy pinching condition r 0 sigma n k max where sigma n in frac 1 4 1 is an explicit positive constant depending only on n then m must be isometric to a spherical space form moreover we prove that if an n ge 4 dimensional compact einstein manifold satisfies k min ge eta n r 0 where eta n in frac 1 4 1 is an explicit positive constant then m is locally symmetric it should be emphasized that the pinching constant eta n is optimal when n is even we then obtain some rigidity theorems for einstein manifolds under n 2 th ricci curvature and normalized scalar curvature pinching conditions finally we extend the theorems above to einstein submanifolds in a riemannian manifold and prove that if m is an n ge 4 dimensional compact einstein submanifold in the simply connected space form f n c with constant curvature c ge 0 and the normalized scalar curvature r 0 of m satisfies r 0 frac a n a n 4n 8 c h 2 where a n n 3 5n 2 8n and h is the mean curvature of m then m is isometric to a standard n sphere

pyramid ricci flow in higher dimensions in this paper we construct a pyramid ricci flow starting with a complete riemannian manifold m n g 0 that is pic1 or more generally satisfies a lower curvature bound mathrm k ic 1 ge alpha 0 that is instead of constructing a flow on m times 0 t we construct it on a subset of space time that is a union of parabolic cylinders mathbb b g 0 x 0 k times 0 t k for each k in mathbb n where t k downarrow 0 and prove estimates on the curvature and riemannian distance more generally we construct a pyramid ricci flow starting with any noncollapsed mathrm ic 1 limit space and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi holder

mean curvature flow of pinched submanifolds to spheres the evolution of hypersurfaces by their mean curvature has been studied by many authors since the appearance of gerhard huisken s seminal paper hu1 more recently mean curvature flow of higher codimension submanifolds has also received attention in this paper we prove a result analogous to that of hu1 for submanifolds of any codimension let f0 n rn k be a smooth immersion of a compact manifold the mean curvature flow with initial condition f0 is a smooth family of immersions f 0 t rn k satisfying

thermodynamic capacity of quantum processes thermodynamics imposes restrictions on what state transformations are possible in the macroscopic limit of asymptotically many independent copies of a state as for instance in the case of an ideal gas the possible transformations become reversible and are fully characterized by the free energy in this letter we present a thermodynamic resource theory for quantum processes that also becomes reversible in the macroscopic limit a property that is especially rare for a resource theory of quantum channels we identify a unique single letter and additive quantity the thermodynamic capacity that characterizes the thermodynamic value of a quantum channel in the sense that the work required to simulate many repetitions of a quantum process employing many repetitions of another quantum process becomes equal to the difference of the respective thermodynamic capacities on a technical level we provide asymptotically optimal constructions of universal implementations of quantum processes a challenging aspect of this construction is the apparent necessity to coherently combine thermal engines that would run in different thermodynamic regimes depending on the input state our results have applications in quantum shannon theory by providing a generalized notion of quantum typical subspaces and by giving an operational interpretation to the entropy difference of a channel

ancient solutions to the ricci flow with pinched curvature we show that any ancient solution to the ricci flow which satisfies a suitable curvature pinching condition must have constant sectional curvature

min and max relative entropies and a new entanglement monotone two new relative entropy quantities called the min and max relative entropies are introduced and their properties are investigated the well known min and max entropies introduced by renner are obtained from these we define a new entanglement monotone which we refer to as the max relative entropy of entanglement and which is an upper bound to the relative entropy of entanglement we also generalize the min and max relative entropies to obtain smooth min and max relative entropies these act as parent quantities for the smooth renyi entropies eth zurich ph d dissertation 2005 and allow us to define the analogues of the mutual information in the smooth renyi entropy framework further the spectral divergence rates of the information spectrum approach are shown to be obtained from the smooth min and max relative entropies in the asymptotic limit

independence of work and entropy for equal energetic finite quantum systems passive state energy as an entanglement quantifier although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic ee states in the asymptotic limit for the finite quantum systems the relation is not so linear and requires detailed investigation toward this we have considered a resource theoretic framework taking the energy preserving operations epos as free to compare the amount of extractable work from two different quantum states under the epo majorization becomes a necessary criterion for state transformation it is also shown that the passive state energy is a concave function and for ee states it becomes proportional to the ergotropy in absolute sense invariance of the passive state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states furthermore due to the nonadditivity of passive state energy for the different system hamiltonians one can generate vidal s monotones which would give the optimal probability for pure entangled state transformation this measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three qubit pure entangled states

a unified theory of the point groups ii the general projective representations and their application to space groups the general expressions of all inequivalent irreducible projective representations of crystallographic and noncrystallographic point groups except for the icosahedral group are given in terms of the vector representations of the proper double point groups its application to the representations of the space group of wave vector is discussed construction of the basis sets is discussed

strong converse for the classical capacity of entanglement breaking and hadamard channels via a sandwiched renyi relative entropy a strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel along with a corresponding achievability statement for rates below the capacity such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication here we show that such a strong converse theorem holds for the classical capacity of all entanglement breaking channels and all hadamard channels the complementary channels of the former these results follow by bounding the success probability in terms of a sandwiched renyi relative entropy by showing that this quantity is subadditive for all entanglement breaking and hadamard channels and by relating this quantity to the holevo capacity prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results

a unified theory of the point groups and their general irreducible representations point groups and their general irreducible vector and projective representations are characterized by the subgroup conditions for su 2 in a unified scheme these conditions are given by simple polynomial equations imposed on the matrix elements of the 2 2 unitary matrices of su 2 the general irreducible representations for the point groups d dn with arbitrary integer n 2 o and t are given by four simple and effective tables

reduced dynamics need not be completely positive the reduced dynamics of a quantum system in contact with a reservoir is generally thought to be completely positive this is certainly true if product initial conditions are used to define the dynamics we show that with correlated initial conditions it need not be so in this case the dynamics can properly be defined only on a subset of initial system states extension by linearity to all possible initial states is trivially possible but the extension may not be physically realizable and may not even be positive let alone completely positive