an obstruction based approach to the kochen specker theorem in isham and butterfield 1998 int j theor phys 37 2669 733 it was shown that the kochen specker theorem can be written in terms of the non existence of global elements of a certain varying set over the category of boolean subalgebras of projection operators on some hilbert space in this paper we show how obstructions to the construction of such global elements arise and how this provides a new way of looking at proofs of the theorem

maximal violation of bell s inequalities for continuous variable systems we generalize bell s inequalities to biparty systems with continuous quantum variables this is achieved by introducing the bell operator in perfect analogy to the usual spin 1 2 systems it is then demonstrated that two mode squeezed vacuum states display quantum nonlocality by using the generalized bell operator in particular the original einstein podolsky rosen states which are the limiting case of the two mode squeezed vacuum states can maximally violate bell s inequality due to clauser horne shimony and holt the experimental aspect of our scheme is briefly considered

how does a box work a study in the qualitative dynamics of solid objects this paper is an in depth study of qualitative physical reasoning about one particular scenario using a box to carry a collection of objects from one place to another specifically we consider the plan plan1 load objects ucargo into box obox one by one carry obox from location l1 to location l2 we present qualitative constraints on the shape starting position and material properties of ucargo and obox and on the characteristics of the motion that suffice to make it virtually certain that plan1 can be successfully executed we develop a theory consisting mostly of first order statements together with two default rules that supports an inference of the form if conditions xyz hold and the agent attempts to carry out plan1 then presumably he will succeed our theory is elaboration tolerant in the sense that carrying out the analogous inference for carrying objects in boxes with lids in boxes with small holes or on trays can reuse much of the same knowledge the theory integrates reasoning about continuous time euclidean space commonsense dynamics of solid objects and semantics of partially specified plans

some qualitative questions on the equation div a x u u f x u abstract in this article we establish several applications of picone s identity for the operator of the form d i v a x u u such as hardy type inequality sturmian comparison theorem monotonicity property of the first eigenvalue nonexistence of positive supersolutions and caccioppoli inequality under certain conditions on a

proofs of the kochen specker theorem based on a system of three qubits a number of new proofs of the kochen specker theorem are given based on the observables of the three qubit pauli group each proof is presented in the form of a diagram from which it is obvious by inspection each of our observable based proofs leads to a system of projectors and bases that generally yields a large number of parity proofs of the kochen specker theorem some examples of such proofs are given and some of their applications are discussed

proposed experimental tests of the bell kochen specker theorem for a two particle two state system sets of compatible propositions exist for which quantum mechanics and noncontextual hidden variable theories make conflicting predictions for every individual system whatever its quantum state this permits a simple all or nothing state independent experimental verification of the bell kochen specker theorem

discord and nonclassicality in probabilistic theories quantum discord quantifies nonclassical correlations in quantum states we introduce discord for states in causal probabilistic theories inspired by the original definition proposed by h ollivier and w h zurek phys rev lett 88 017901 2001 we show that the only probabilistic theory in which all states have null discord is classical probability theory non null discord is then not just a quantum feature but a generic signature of nonclassicality

stronger two observer all versus nothing violation of local realism we introduce a two observer all versus nothing proof of bell s theorem which reduces the number of required quantum predictions from 9 a cabello phys rev lett 87 010403 2001 z b chen et al phys rev lett 90 160408 2003 to 4 provides a greater amount of evidence against local realism reduces the detection efficiency requirements for a conclusive experimental test of bell s theorem and leads to a bell inequality which resembles mermin s inequality for three observers n d mermin phys rev lett 65 1838 1990 but requires only two observers

bipartite all versus nothing proofs of bell s theorem with single qubit measurements if n qubits were distributed between 2 parties which quantum pure states and distributions of qubits would allow all versus nothing or greenberger horne zeilinger like proofs of bell s theorem using only single qubit measurements we show a necessary and sufficient condition for the existence of these proofs for any number of qubits and provide all distinct proofs up to n 7 qubits remarkably there is only one distribution of a state of n 4 qubits and six distributions each for a different state of n 6 qubits which allow these proofs

multipartite nonlocality as a resource and quantum correlations having indefinite causal order the characterization of quantum correlations in terms of information theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource while bipartite entanglement and bell inequality violation in this setting have been extensively studied relatively little is known about their multipartite counterpart in this paper we apply and adapt the recently proposed definitions of multipartite nonlocality bancal et al 2013 phys rev a 88 014102 to the three and four partite scenarios to gain new insight on the resource aspect of multipartite nonlocal quantum correlations specifically we show that reproducing certain tripartite quantum correlations requires mixtures of classical resources be it the ability to change the groupings or the time orderings of measurements thus when seen from the perspective of biseparable one way classical signaling resources certain tripartite quantum correlations do not admit a definite causal order in the four partite scenario we obtain a superset description of the set of biseparable correlations which can be produced by allowing two groups of bipartite non signaling resources quantum violation of the resulting bell like inequalities is investigated as a byproduct we obtain some new examples of device independent witnesses for genuine four partite entanglement and also device independent witnesses that allow one to infer the structure of the underlying multipartite entanglement this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

two simple proofs of the kochen specker theorem a new proof of the kochen specker theorem uses 33 rays instead of 117 in the original proof if the number of dimensions is increased from 3 to 4 only 24 rays are needed

entropic tests of multipartite nonlocality and state independent contextuality we introduce a multipartite extension of an information theoretic distance introduced by zurek nature london 341 119 1989 we use it to develop a new tool for studying quantum correlations from an information theoretic perspective in particular we derive entropic tests of multipartite nonlocality for three qubits and for an arbitrary even number of qubits as well as a test of state independent contextuality in addition we rederive the tripartite mermin inequality and a state independent noncontextuality inequality by cabello phys rev lett 101 210401 2008 this suggests that the information theoretic distance approach to multipartite nonlocality and state independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions

perfect commuting operator strategies for linear system games linear system games are a generalization of mermin s magic square game introduced by cleve and mittal they show that perfect strategies for linear system games in the tensor product model of entanglement correspond to finite dimensional operator solutions of a certain set of non commutative equations we investigate linear system games in the commuting operator model of entanglement where alice and bob s measurement operators act on a joint hilbert space and alice s operators must commute with bob s operators we show that perfect strategies in this model correspond to possibly infinite dimensional operator solutions of the non commutative equations the proof is based around a finitely presented group associated with the linear system which arises from the non commutative equations

inequalities for experimental tests of the kochen specker theorem we derive inequalities for n partite states under the assumption that the hidden variable theoretical joint probability distribution for any pair of commuting observables is equal to the quantum mechanical one fine showed that this assumption is connected to the no hidden variables theorem of kochen and specker ks theorem these inequalities give a way to experimentally test the ks theorem the fidelity to the bell states which is larger than 1 2 is sufficient for the experimental confirmation of the ks theorem hence the werner state is enough to test experimentally the ks theorem furthermore it is possible to test the ks theorem experimentally using uncorrelated states an n partite uncorrelated state violates the n partite inequality derived here by an amount that grows exponentially with n

principal eigenvalues and sturm comparison via picone s identity we characterize the principal eigenvalues and eigenfunctions in rn and present comparison results for higher dimensional p laplacian our main tool is picone s identity in this way we extend several recent results on spectral and comparison properties for differential equations

hedging bets with correlated quantum strategies this paper studies the potential advantages of correlated answers in hypothetical tests of a simple interactive type in these tests an individual is presented with a question to which he or she must respond with an answer leading to an outcome of pass or fail in quantum information theoretic variants of these tests we show it is possible for an individual to correlate their answers across multiple tests in a way that produces a striking non classical behaviour specifically there exist tests for which no strategy can lead to the outcome pass with certainty but where answers to multiple independently administered tests can be correlated so that at least one test is passed with certainty this phenomenon which gives rise to a perfect form of hedging when considered in a game theoretic setting is quantum in nature it is not possible in classical variants of the tests we consider

simple unified form for the major no hidden variables theorems two examples are given that substantially simplify the no hidden variables theorem of kochen and specker greatly reducing the number of observables considered and requiring no intricate geometric argument while one of the examples also obeys a more powerful version of bell s theorem the other does not the examples provide a new perspective on both of these fundamental theorems and on the relation between them

bell kochen specker theorem for any finite dimension the bell kochen specker theorem against non contextual hidden variables can be proved by constructing a finite set of totally non colourable directions as kochen and specker did in a hilbert space of dimension n 3 we generalize kochen and specker s set to hilbert spaces of any finite dimension in a three step process that shows the relationship between different kinds of proofs continuum probabilistic state specific and state independent of the bell kochen specker theorem at the same time this construction of a totally non colourable set of directions in any dimension explicitly solves the question raised by zimba and penrose about the existence of such a set for n 5

qualitative rigid body mechanics abstract we present a theory of qualitative rigid body mechanics and describe a program that uses this theory to compute qualitative rigid body dynamic simulations the program works directly from a qualitative representation of geometry qualitative configuration space without need of any metric information the program can handle devices that are composed of an arbitrary number of fixed axis components and springs with driving inputs coming from both applied motions and forces the program employs quasi static assumptions i e inertia free motion inelastic collisions and frictionless contacts it employs a new qualitative representation for forces that reduces ambiguity in force sums and hence reduces unnecessary branching

planning for conjunctive goals abstract the problem of achieving conjunctive goals has been central to domain independent planning research the nonlinear constraint posting approach has been most successful previous planners of this type have been complicated heuristic and ill defined i have combined and distilled the state of the art into a simple precise implemented algorithm tweak which i have proved correct and complete i analyze previous work on domain independent conjunctive planning in retrospect it becomes clear that all conjunctive planners linear and nonlinear work the same way the efficiency and correctness of these planners depends on the traditional add delete list representation for actions which drastically limits their usefulness i present theorems that suggest that efficient general purpose planning with more expressive action representations is impossible and suggest ways to avoid this problem

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

necessary conditions for extended noncontextuality in general sets of random variables in this paper we explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by kujala et al phys rev lett 115 150401 2015 using graph theoretical terms this extended definition avoids the assumption of the pre sheaf or non disturbance condition which states that if two contexts overlap then the marginal distribution obtained for the intersection must be the same a restriction that will never be perfectly satisfied in real experiments with this we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non disturbance condition is satisfied

nonmonotonic logic and temporal projection abstract nonmonotonic formal systems have been proposed as an extension to classical first order logic that will capture the process of human default reasoning or plausible inference through their inference mechanisms just as modus ponens provides a model for deductive reasoning but although the technical properties of these logics have been studied in detail and many examples of human default reasoning have been identified for the most part these logics have not actually been applied to practical problems to see whether they produce the expected results we provide axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning thus presumably amenable to representation in nonmonotonic logic upon examining the resulting nonmonotonic theories however we find that the inferences permitted by the logics are not those we had intended when we wrote the axioms and in fact are much weaker this problem is shown to be independent of the logic used nor does it depend on any particular temporal representation upon analyzing the failure we find that the nonmonotonic logics we considered are inherently incapable of representing this kind of default reasoning the first part of the paper is an expanded version of one that appeared in the 1986 aaai proceedings the second part reports on several responses to our result that have appeared since the original paper was published

geometry of uncertainty relations for linear combinations of position and momentum for a quantum particle with a single degree of freedom we derive preparational sum and product uncertainty relations satisfied by n linear combinations of position and momentum observables the state independent bounds depend on their degree of incompatibility defined by the area of a parallelogram in an n dimensional coefficient space maximal incompatibility occurs if the observables give rise to regular polygons in phase space we also conjecture a hirschman type uncertainty relation for n observables linear in position and momentum generalizing the original relation which lower bounds the sum of the position and momentum shannon entropies of the particle

constraints on quantum hidden variables and the bohm theory the no hidden variables arguments of mermin and peres 1990 are assessed in the light of the bohm formulation of quantum theory

state independent proof of kochen specker theorem with 13 rays quantum contextuality as proved by kochen and specker and also by bell should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified however for the simplest system capable of exhibiting contextuality a qutrit the quantum contextuality is verified only state dependently in experiment because too many at least 31 observables are involved in all the known state independent tests here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states thus our inequality facilitates a state independent test of the quantum contextuality for an indivisible quantum system we also provide a record breaking state independent proof of the kochen specker theorem with 13 directions determined by 26 points on the surface of a magic cube

general conditions for maximal violation of non contextuality in discrete and continuous variables the contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables an important property of such observables is that their expectation value can be expressed in terms of probabilities for obtaining two exclusive outcomes examples of such inequalities have been constructed using either observables with a dichotomic spectrum or using periodic functions obtained from displacement operators in phase space here we identify the general conditions on the spectral decomposition of observables demonstrating state independent contextuality of quantum mechanics our results not only unify existing strategies for maximal violation of state independent non contextuality inequalities but also lead to new scenarios enabling such violations among the consequences of our results is the impossibility of having a state independent maximal violation of non contextuality in the peres mermin scenario with discrete observables of odd dimensions

mermin pentagrams arising from veldkamp lines for three qubits we study the geometry of the space of mermin pentagrams objects that are used to rule out the existence of noncontextual hidden variable theories as alternatives to quantum theory it is shown that this space of 12 096 possible pentagrams is organized into 1008 families with each family containing a double six of pentagrams the 1008 families are connected to a special set of veldkamp lines in the veldkamp space for three qubits an object well known to finite geometers but has only been introduced to physics recently due to the transitive action of the symplectic group on this set of veldkamp lines it is enough to study only one canonical double six configuration of pentagrams we prove that the geometry of this double six configuration is encapsulated in the weight diagram of the 20 dimensional irreducible representation of the group as an interesting by product of our approach we show that mermin pentagrams and a class of mermin squares labelled by three qubit pauli operators are inherently related we conjecture that by studying the representation theoretic content of other veldkamp lines of the veldkamp space for n qubits makes it possible to find new contextual configurations in a systematic manner

the construction of kochen specker noncolourable sets in higher dimensional space from corresponding sets in lower dimension modification of cabello estebaranz and garcia alcaine s method by re examination of cabello estebaranz and garcia alcaine s method ceg for constructing a ray set which gives a proof of kochen specker theorem in a higher dimension from an already known set in a lower dimension a more refined method is derived in the construction of ray sets of higher dimension we need fewer rays than in ceg by using the method an analytical proof of the ks noncolourability of ray sets in real hilbert spaces is also given whose ks noncolourability was found by ceg by computer calculation

the veldkamp space of multiple qubits we introduce a point line incidence geometry in which the commutation relations of the real pauli group of multiple qubits are fully encoded its points are pairs of pauli operators differing in sign and each line contains three pairwise commuting operators any of which is the product of the other two up to sign we study the properties of its veldkamp space enabling us to identify subsets of operators which are distinguished from the geometric point of view these are geometric hyperplanes and pairwise intersections among the geometric hyperplanes one can find the set of self dual operators with respect to the wootters spin flip operation well known from studies concerning multiqubit entanglement measures in the two and three qubit cases a class of hyperplanes gives rise to mermin squares and other generalized quadrangles in the three qubit case the hyperplane with points corresponding to the 27 wootters self dual operators is just the underlying geometry of the e6 6 symmetric entropy formula describing black holes and strings in five dimensions

nonlocal games and quantum permutation groups we present a strong connection between quantum information and quantum permutation groups specifically we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups and then show that this is equivalent to the previously defined notion of quantum isomorphism corresponding to perfect quantum strategies to the isomorphism game moreover we show that two connected graphs x and y are quantum isomorphic if and only if there exists x v x and y v y that are in the same orbit of the quantum automorphism group of the disjoint union of x and y this connection links quantum groups to the more concrete notion of nonlocal games and physically observable quantum behaviours we exploit this link by using ideas and results from quantum information in order to prove new results about quantum automorphism groups and about quantum permutation groups more generally in particular we show that asymptotically almost surely all graphs have trivial quantum automorphism group furthermore we use examples of quantum isomorphic graphs from previous work to construct an infinite family of graphs which are quantum vertex transitive but fail to be vertex transitive answering a question from the quantum group literature our main tool for proving these results is the introduction of orbits and orbitals orbits on ordered pairs of quantum permutation groups we show that the orbitals of a quantum permutation group form a coherent configuration algebra a notion from the field of algebraic graph theory we then prove that the elements of this quantum orbital algebra are exactly the matrices that commute with the magic unitary defining the quantum group we furthermore show that quantum isomorphic graphs admit an isomorphism of their quantum orbital algebras which maps the adjacency matrix of one graph to that of the other

family of bell like inequalities as device independent witnesses for entanglement depth we present a simple family of bell inequalities applicable to a scenario involving arbitrarily many parties each of which performs two binary outcome measurements we show that these inequalities are members of the complete set of full correlation bell inequalities discovered by werner wolf ifmmode dot z else z fi ukowski brukner for scenarios involving a small number of parties we further verify that these inequalities are facet defining for the convex set of bell local correlations moreover we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many body entangled in other words our bell inequalities when supplemented with the appropriate quantum bounds naturally serve as device independent witnesses for entanglement depth allowing one to certify genuine k partite entanglement in an arbitrary n ensuremath ge k partite scenario without relying on any assumption about the measurements being performed or the dimension of the underlying physical system a brief comparison is made between our witnesses and those based on some other bell inequalities as well as quantum fisher information a family of witnesses for genuine k partite nonlocality applicable to an arbitrary n ensuremath ge k partite scenario based on our bell inequalities is also presented

bellʼs inequality and extremal non local box from hardyʼs test for non locality bell showed 50 years ago that quantum theory is non local via his celebrated inequalities turning the issue of quantum non locality from a matter of taste into a matter of test years later hardy proposed a test for non locality without inequality which is a kind of something versus nothing argument hardy s test for n particles induces an n partite bell s inequality with two dichotomic local measurements for each observer which has been shown to be violated by all entangled pure states our first result is to show that the bell hardy inequality arising form hardy s non locality test is tight for an arbitrary number of parties i e it defines a facet of the bell polytope in the given scenario on the other hand quantum theory is not that non local since it forbids signaling and even not as non local as allowed by non signaling conditions i e quantum mechanical predictions form a strict subset of the so called non signaling polytope in the scenario of each observer measuring two dichotomic observables fritz established a duality between the bell polytope and the non signaling polytope tight bell s inequalities the facets of the bell polytope are in a one to one correspondence with extremal non signaling boxes the vertices of the non signaling polytope our second result is to provide an alternative and more direct formula for this duality as an example the tight bell hardy inequality gives rise to an extremal non signaling box that serves as a natural multipartite generalization of popescu rohrlich box this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

the morita theory of quantum graph isomorphisms we classify instances of quantum pseudo telepathy in the graph isomorphism game exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups specifically we show that graphs quantum isomorphic to a given graph are in bijective correspondence with morita equivalence classes of certain frobenius algebras in the category of finite dimensional representations of the quantum automorphism algebra of that graph we show that such a frobenius algebra may be constructed from a central type subgroup of the classical automorphism group whose action on the graph has coisotropic vertex stabilisers in particular if the original graph has no quantum symmetries quantum isomorphic graphs are classified by such subgroups we show that all quantum isomorphic graph pairs corresponding to a well known family of binary constraint systems arise from this group theoretical construction we use our classification to show that of the small order vertex transitive graphs with no quantum symmetry none is quantum isomorphic to a non isomorphic graph we show that this is in fact asymptotically almost surely true of all graphs

a hidden variables versus quantum mechanics experiment in the light of the bell kochen specker theorem we examine a feasible experimental test in order to discriminate between non contextual hidden variables and some probabilistic predictions of quantum mechanics

optimal classical simulation of state independent quantum contextuality simulating quantum contextuality with classical systems requires memory a fundamental yet open question is what is the minimum memory needed and therefore the precise sense in which quantum systems outperform classical ones here we make rigorous the notion of classically simulating quantum state independent contextuality qsic in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite qsic set we obtain the minimum memory needed to simulate arbitrary qsic sets via classical systems under the assumption that the simulation should not contain any oracular information in particular we show that while classically simulating two qubits tested with the peres mermin set requires log 2 24 4 585 bits simulating a single qutrit tested with the yu oh set requires at least 5 740 bits