There has been recent interest in whether the concept of quantum contextuality can be extended to systems with disturbance or signaling while retaining the essential properties of standard contextuality. Dzhafarov and Kujala (arXiv:2302.11995) offer a provocative argument that the answer is always affirmative: If standard contextuality satisfies some principle that extended contextuality does not, then that principle must be `non-substantive' in that it depends on a superficial choice of representation. Their argument is based on a ``consistification'' procedure that maps all systems to nondisturbing ones and that preserves contextuality. This paper raises several objections to their argument, including that it neglects how substantive principles change their expression under a change of representation, that it begs the question by presuming the principles are based on non-substantive transformations, and that the argument applies universally to arbitrary extensions of contextuality.
Exploring the graph approach, we restate the extended definition of noncontextuality provided by the contextuality-by-default framework. This extended definition avoids the assumption of nondisturbance, which states that whenever two contexts overlap, the marginal distribution obtained for the intersection must be the same. We show how standard tools for characterizing contextuality can also be used in this extended framework for any set of measurements and, in addition, we also provide several conditions that can be tested directly in any contextuality experiment. Our conditions reduce to tra…
In this paper we study an application of an information distance between two measurements to the problem of non-contextuality and local realism. We postulate the triangle principle which states that any information distance is well defined on any pair of measurements, even if the two measurements cannot be jointly performed. As a consequence, the triangle inequality for this distance is obeyed for any three measurements. This simple principle is valid in any classical realistic theory, however it does not hold in quantum theory. It allows us to re-derive in an astonishingly simple way a large …
We show that the main idea behind contextuality-by-default (CbD), i.e., the assumption that a physical measurement has to be understood as a contextual collection of random variables, is implicit in the compatibility-hypergraph approach to contextuality (CA) and use this result to develop in the latter important concepts which were introduced in the former. We introduce in CA the non-degeneracy condition, which is the analogous of consistent connectedness, and prove that this condition is, in general, weaker than non-disturbance condition. The set of non-degenerate behaviours defines a polytop…
In a recent article entitled "A simple explanation of the quantum violation of a fundamental inequality," Cabello proposes a condition on a class of probabilistic models that, he claims, gives the same bound on contextuality for the KCBS inequality as quantum mechanics, and also rules out PR-box nonlocality. He conjectures that the condition will also reproduce quantum limits on contextuality in other scenarios. Here we show that the proposed principle is actually too weak to derive these results. Cabello has implicitly assumed in the proofs that if all pairs in a set of events are pairwise ex…
In the paper, a value assignment for projection operators relating to a quantum system is equated with assignment of truth-values to the propositions associated with these operators. In consequence, the Kochen-Specker theorem (its localized variant, to be exact) can be treated as the statement that a logic of those projection operators does not obey the principle of bivalence. This implies that such a logic has a gappy (partial) semantics or many-valued semantics.
This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis -- i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the (reduced, spin-only) wave function of the system, which is conditional on the realized location values of the particles. In this way, the unavoidable contextua…
In quantum physics, the notion of contextuality has a variety of interpretations which are typically associated with the names of their inventors, say Bohr, Bell, Kochen and Specker, and recently Dzhafarov. In fact, Bohr was the first who pointed to contextuality of quantum measurements as a part of formulation of his principle of complementarity. (Instead of "contextuality", he considered dependence on "experimental conditions.") Unfortunately, the contextuality counterpart of the complementarity principle was overshadowed by the issue of incompatibility of observables. And the interest for c…
Quantum mechanics allows only certain sets of experimental results (or "probabilistic models") for Bell-type quantum non-locality experiments. A derivation of this set from simple physical or information theoretic principles would represent an important step forward in our understanding of quantum mechanics, and this problem has been intensely investigated in recent years. "Macroscopic locality," which requires the recovery of locality in the limit of large numbers of trials, is one of several principles discussed in the literature that place a bound on the set of quantum probabilistic models.…
Recently many simple principles have been proposed that can explain quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments. However, few implications between these principles are known. Here it is shown that lack of irreducible third-order interference (a generalisation of the idea that no probabilistic interference remains unaccounted for once we have taken into account interference between pairs of slits in a $n$-sit experiment) implies the principle known as the E principle or Consistent Exclusivity (that, if each pair of a set of exp…
In this essay I develop quantum contextuality as a potential candidate for Wheeler's universal regulating principle, arguing -- \textit{contrary} to Wheeler -- that this ultimately implies that `bit' comes from `it.' In the process I develop a formal definition of physical determinism in the languages of domain theory and category theory.
The totalitarian principle establishes that `anything not forbidden is compulsory'. The problem of quantum correlations is explaining what selects the set of quantum correlations for a Bell and Kochen-Specker (KS) contextuality scenario. Here, we show that two assumptions and a version of the totalitarian principle lead to the quantum correlations. The assumptions are that there is a non-empty set of correlations for any KS contextuality scenario and a statistically independent realisation of any two KS experiments. The version of the totalitarian principle says that any correlation not forbid…
Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently to actual and possible properties of the system. By means of a topological argument, more precisely in terms of the existence of sections of sheaves, we give an extended version of Kochen-Specker theorem over this new structure. This allows us to prove that contextuality remains a central feature even in the enriched propositional system.
Modal quantum theory (MQT) is a simplified cousin of ordinary Hilbert space quantum theory. We show that two important theorems of actual quantum theory, the Kochen-Specker theorem excluding non-contextual hidden variables and the Conway-Kochen "free will theorem" about entangled systems, have direct analogues in MQT. The proofs of these analogue theorems are similar to, but much simpler than, the originals. We also show that the structure of possible measurement results for an entangled system in MQT cannot be represented by probability assignments satisfying the no-signaling principle, such …
If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not re…
We explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by J. 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 vari…
In Itamar Pitowsky's reading of the Gleason and the Kochen-Specker theorems, in particular, his Logical Indeterminacy Principle, the emphasis is on the value indefiniteness of observables which are not within the preparation context. This is in stark contrast to the prevalent term {\em contextuality} used by many researchers in informal, heuristic yet omni-realistic and potentially misleading ways. This paper discusses both concepts and argues in favor of value indefiniteness in all but a continuum of contexts intertwining in the vector representing a single pure (prepared) state. Even more re…
A unified view on the phenomenon of monogamy exhibited by Bell inequalities and non-contextuality inequalities arising from the no-signaling and no-disturbance principles is presented using the graph-theoretic method introduced in \textit{Phys. Rev. Lett. 109, 050404 (2012)}. We propose a novel type of trade-off, namely Bell inequalities that do not exhibit monogamy features of their own can be activated to be monogamous by the addition of a local contextuality term. This is illustrated by means of the well-known $\mathcal{I}_{3322}$ inequality, and reveals a resource trade-off between biparti…
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entro…
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the non-contextual hidden variable theories in which the properties of a system have pre-defined values which are independent of the measurement contextual. However, the Kochen-Specker theorem showed that such non-contextual hidden variable theories are in conflict with quantum mechanics. Recently, a state-independent inequality satisfied by non-contextual hidden variable t…
The two state vector formalism (TSVF) was proposed by Aharonov, Bergmann, and Lebowitz (ABL) to provide a way for the counterfactual assignment of the probabilities of outcomes of contemplated but unperformed measurements on quantum systems. This formalism underlies various aspects of foundations of quantum theory and has been used significantly in the development of weak values and several proofs of quantum contextuality. We consider the application of TSVF, with pre- and post-selection (PPS) and the corresponding ABL rule, as a means to unearth quantum contextuality. We use the principle of …
The most promising candidate for being the fundamental principle of quantum contextuality is the Exclusivity principle, which states that the sum of the probabilities of a set of pairwise exclusive events cannot exceed 1. By itself, the Exclusivity principle singles out the maximum quantum value for some important Bell and noncontextuality inequalities. We can get better results if we apply the E principle to more sophisticated scenarios. This happens because this principle exhibits activation effects: a distribution satisfying this principles does not necessarily satisfy it when combined with…
Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in other theories, whenever there is an experiment to measure $A$ simultaneously with $B$, another to measure $B$ with $C$, and another to measure $A$ with $C$, there is always an experiment to measure all of them simultaneously. This property implies that quantum theory satisfies a seemingly irrelevant restriction called the exclusivity (E) principle which, sur…
In this paper we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no-disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs …
We argue that Anton Zeilinger's "foundational conceptual principle" for quantum mechanics according to which an elementary system carries one bit of information is an idealistic principle, which should be replaced by a realistic principle of contextuality. Specific properties of quantum systems are a consequence of impossibility to speak about them without reference to the tools of their observation (identification) and, consequently, context in which these tools are applied. In particular, the assumption of non-locality is not required to explain quantum correlation. Correlated quantum events…
We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two---producing an exterior, or Grassmann, algebra---which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each …
Purdue University（普渡大学）；University of Jyväskylä（于韦斯屈莱大学）
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered stochastically unrelated, possessing no joint distribution. An input that does not directly influence an output creates a context for the latter. Any constraint imposed on the dependence of random outputs on inputs can be characterized by considering all possible couplings (joint distributions) imposed on stochastically unrelated outputs. The target applica…
Contextuality means non-existence of a joint distribution for random variables recorded under mutually incompatible conditions, subject to certain constraints imposed on how the identity of these variables may change across these conditions. In simple quantum systems contextuality is indicated by violations of Bell-type or Leggett-Garg-type inequalities. These inequalities, however, are predicated on the assumption of no-signaling, defined as invariance of the distributions of measurement results with respect to other (e.g., earlier in time) measurements' settings. Signaling makes the inequali…
We develop a hypergraph-theoretic framework for Spekkens contextuality applied to Kochen-Specker (KS) type scenarios that goes beyond the Cabello-Severini-Winter (CSW) framework. To do this, we add new hypergraph-theoretic ingredients to the CSW framework. We then obtain noise-robust noncontextuality inequalities in this generalized framework by applying the assumption of (Spekkens) noncontextuality to both preparations and measurements. The resulting framework goes beyond the CSW framework, both conceptually and technically. On the conceptual level: 1) we relax the assumption of outcome deter…
In this thesis we use the language of sheaf theory in order to develop a deeper understanding of some of the fundamental differences - such as entanglement, contextuality and non-locality - between quantum and classical physics. We first present, based on the work of Abramsky and Brandenburger, how sheaves, defined over certain posets of physically meaningful contexts, give a natural setting for capturing and analysing important quantum mechanical phenomena, such as quantum non-locality and contextuality. We also describe how this setting naturally leads to a three level hierarchy of quantum c…
Characterizing quantum correlations in terms of information-theoretic principles is a popular chapter of quantum foundations. Traditionally, the principles adopted for this scope have been expressed in terms of conditional probability distributions, specifying the probability that a black box produces a certain output upon receiving a certain input. This framework is known as "device-independent". Another major chapter of quantum foundations is the information-theoretic characterization of quantum theory, with its sets of states and measurements, and with its allowed dynamics. The different fr…
The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different contexts may have different distributions, due to contextual biases in experimental design or physical interactions (signaling): a system of measurements has a maximally noncontextual description if they can be imposed a joint distribution on in which the measurements of any one property in different contexts are equal to each other with the maximal probabi…
The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.
The action reaction principle is violated by the projection of state in some simple quantum measurements. A formulation of Quantum Mechanics in an extended phase space is proposed in order to restore the action reaction principle. All predictions of the standard theory are reproduced. Observable effects of an accompanying de Broglie wave are also predicted.
The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a distribution of probability in a space of local variables can not reproduce the quantum correlations. An extended phase space is defined in an alternative formulation of Quantum Mechanics. Quantum states are represented by a complex va\-lued distribution of amplitude, so that Bell's theorems do not apply.
Quantum technologies can be presented to the public with or without introducing a strange trait of quantum theory responsible for their non-classical efficiency. Traditionally the message was centered on the superposition principle, while entanglement and properties such as contextuality have been gaining ground recently. A less theoretical approach is focused on simple protocols that enable technological applications. It results in a pragmatic narrative built with the help of the resource paradigm and principle-based reconstructions. I discuss the advantages and weaknesses of these methods. T…
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe electromagnetic (3+1)-soliton-like objects in vacuum and in the presence of continuous media (external fields), exchanging energy-momentum with the electromagnetic field.
We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order coupling to the gravitational field. In particular, a new force due to the octupole moment is obtained. The action also yields the gravitationally induced phase shifts in quantum interference experiments due to the coupling of all multipole moments.
We present the exact solution of the three-dimensional Duffin--Kemmer--Petiau oscillator for both spin 0 and spin 1 cases, with the presence of minimal uncertainty in momentum in anti--de Sitter model. We use the representation of vector spherical harmonics and the Nikiforov--Uvarov method to determine exactly the energy eigenvalues and the eigenfunctions in all cases. Our study of the energy spectrum allows us to define a new interpretation of natural and unnatural parity states of the vector particle and we show the crucial role played by the spin--orbit coupling in this differentiation betw…
