S. M. Roy
We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.
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It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified only in a simplified approach to quantum mechanics when one neglects the fundamental fact that there exist space and time. Mathematical definitions of local realism in the sense of Bell and in the sense of Einstein are given. We demonstrate that if we include into the quantum mechanical formalism the space-time structure in the standard way then quantum mechan…
We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by Mermin, as well as a different type of contextuality proofs based on symmetry transformations. The topological arguments presented can be used in the state-dependent and the state-independent case.
It is argued that 't Hooft's deterministic program does not disenchant the quantum world but rather inspires the incantation of the classical one.
An attempt is made to formulate quantum mechanics (QM) in physical rather than in mathematical terms. It is argued that the appropriate conceptual framework for QM is "contextual objectivity", which includes an objective definition of the quantum state. This point of view sheds new light on topics such as the reduction postulate and the quantum measurement process.
We discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.
In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.
We construct a non-contextual hidden variable model consistent with all the kinematic predictions of quantum mechanics (QM). The famous Bell-KS theorem shows that non-contextual models which satisfy a further reasonable restriction are inconsistent with QM. In our construction, we define a weaker variant of this restriction which captures its essence while still allowing a non-contextual description of QM. This is in contrast to the contextual hidden variable toy models, such as the one by Bell, and brings out an interesting alternate way of looking at QM. The results also relate to the Bohmia…
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical observables with measurement outcomes that cannot be simulated non-contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that \emph{can} be recovered from a non-contextual hidden var…
Contextuality-based quantum key distribution with deterministic single-photon sources
本文利用自组装InAs(Ga)As量子点单光子源产生量子情境性，提出半设备无关量子密钥分发协议，无需理想投影测量，适用于自由空间信道，推动实用量子通信。
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.
In this reply, we point out that the claim by De Zela[2] is unjustified because the setup he discusses is \emph{not} equivalent to the setup analysed in our paper[1]. Hence his subsequent argument claiming the reproducibility of our demonstrated quantum effect of path-spin contextuality by the Kochen-Specker realist model is \emph{not} relevant.
For spin-1/2 particles, using a suitable Mach-Zehnder-type setup with a spin-flipper, we argue that it is a direct consequence of the quantum mechanical treatment that an experimentally verifiable \textit{subensemble} mean of the measured values of an arbitrarily chosen spin variable exhibits dependence on the choice of a comeasurable `path' observable. This, in turn, enables inferring path-spin contextuality at the level of individual measured values of spin that are predetermined using a relevant hidden-variable model applied to our setup.
I examine Pan and Home's reply to my Comment on their proposal for testing noncontextual models. I show that the Kochen-Specker model for a qubit does explain all outcomes of a test based on such a proposal, so that it would be inconclusive about the untenability of realistic, noncontextual models.
Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some of the projectors must have a valuation that depends on the \emph{context} in which they are measured. This motivates the question of \emph{how many} of the projectors must have contextual valuations. In this paper, we demonstrate a bound on what fraction of rank-1 projective measurements on a quantum system must be considered to have context-dependent valua…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in such a way that it may be given an "objective reality". Here we use some ideas about the system dimensionality, taken from quant-ph/0101012, to propose a possible axiomatic approach to QM. In this approach the structure of QM appears as a direct consequence of the non-commutative character of the (classical geometrical) group of "knobs transformations", that …
The Bell-KS theorem and the more recent $ψ$-epistemic \emph{no-go} theorems of QM are discussed in the context of Entropic Dynamics. In doing so we find that the Bell-KS theorem allows for, a perhaps overlooked, hybrid-contextual model of QM in which one set of commuting observables (position in this case) is non-contextual and all other observables are contextual. Entropic Dynamics is in a unique position as compared to other foundational theories of QM because it derives QM using standard techniques in Bayesian probability theory. In this formalism, position is the preferred basis from which…
The most well-known tool for studying contextuality in quantum computation is the n-qubit stabilizer state tableau representation. We provide an extension that describes not only the quantum state, but is also outcome deterministic. The extension enables a value assignment to exponentially many Pauli observables, yet remains quadratic in both memory and computational complexity. Furthermore, we show that the mechanisms employed for contextuality and measurement disturbance are wholly separate. The model will be useful for investigating the role of contextuality in $n$-qubit quantum computation…
The non-extensibility of quantum theory into a theory with improved predictive power is based on a strong assumption of independent free choice, in which the physicists pick a measurement axis independently of anything that couldn't have been caused by their decision. Independent free choice is also at the core of the Nash equilibrium and classical game theory. A more recent line of game-theoretical research based on weakening free choice leads to non-trivial solution concepts with desirable properties such as at-most uniqueness, Pareto optimality, and contextuality. We show how introducing co…
Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is in…
We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and then analyse it's weakness in terms of Bell's explicit hidden variable model of spin one-half particles. We next discuss Gleason's theorem and Kochen-Specker theorem and bring out the troublems with non contextual hidden variable theories. An important role is played by Einstein locality in the discussion of hidden variable theories as was first brought out …
We suggest a contextual realist interpretation of relational quantum mechanics. The principal point is a correct understanding of the concept of reality and taking into account the categorical distinction between the ideal and the real. Within our interpretation, consciousness of the observer does not play any metaphysical role. The proposed approach can also be understood as a return to the Copenhagen interpretation of quantum mechanics, corrected within the framework of contextual realism. The contextual realism allows one to get rid of the metaphysical problems encountered by various interp…
Revisiting the Interpretations of Quantum Mechanics: From FAPP Solutions to Contextual Ontologies
本文通过比较量子力学不同诠释，提出基于情境量化的CSM框架，提供非FAPP本体论以解释不可逆性与测量装置结构。
The Klyachko inequality is an inequality for the probabiities of the values of five observables of a spin-1 particle, which is satisfied by any noncontextual assignment of values to this set of observables, but is violated by the probabilities defined by a certain quantum state. We describe an experiment between two entangled spin-1 particles to test contextuality via a related inequality. We point out that a test of contextuality by measurements on a single particle to confirm the Klyachko inequality requires an assumption of non-disturbance by the measuring instrument, which is avoided in th…
A simple experiment using radioactive decay is proposed to test the possibility of a determinsistic, but chaotic, origin of quantum mechanical randomness.
QBism and relational interpretation of quantum mechanics from the point of view of a contextual quantum realism (CQR)
本文提出语境量子实在论（CQR），区分理想与实在，并批判QBism与关系量子力学混淆二者、隐含反实在论，CQR拒绝将实在还原为客观性。
Contextuality and the fundamental theorems of quantum mechanics
本研究拓展拓扑斯量子力学视角，证明Wigner定理、Gleason定理等四大量子力学基本定理均与语境性相关，并用语境预层语言重述定理，给出适用于冯·诺依曼代数的通用版本，揭示语境性对量子理论结构的核心编码作用。
Quantum mechanics exhibits a very peculiar form of contextuality. Identifying and connecting the simplest scenarios in which more general theories can or cannot be more contextual than quantum mechanics is a fundamental step in the quest for the principle that singles out quantum contextuality. The former scenario corresponds to the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Here we show that there is a simple tight inequality, twin to the KCBS, for which quantum contextuality cannot be outperformed. In a sense, this twin inequality is the simplest tool for recognizing fully contextu…
Contextuality of the probability current in quantum mechanics
本文探讨量子力学中概率电流的上下文性，分析其在不同实验设置下出现的不连续变化，揭示其在相对论中的不可协调性。
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…
Using measurements pertaining to a suitable Mach-Zehnder(MZ) type setup, a curious quantum mechanical effect of contextuality between the path and the polarization degrees of freedom of a polarized photon is demonstrated, without using any notion of realism or hidden variables - an effect that holds good for the product as well as the entangled states. This form of experimental context-dependence is manifested in a way such that at \emph{either} of the two exit channels of the MZ setup used, the empirically verifiable \emph{subensemble} statistical properties obtained by an arbitrary polarizat…
Models for deterministic quantum mechanics of Cartan-Randers type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to Cartan-Randers models provides a framework from which it emerge 1. The invariance under infinitesimal diffeomorphisms of the macroscopic dynamics 2. A mechanism for reduction of the quantum state and 3. The Weak Equivalence Principle.
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 sheaf theoretic description of non-locality and contextuality by Abramsky and Brandenburger sets the ground for a topological study of these peculiar features of quantum mechanics. This viewpoint has been recently developed thanks to sheaf cohomology, which provides a sufficient condition for contextuality of empirical models in quantum mechanics and beyond. Subsequently, a number of studies proposed methods to detect contextuality based on different cohomology theories. However, none of these cohomological descriptions succeeds in giving a full invariant for contextuality applicable to co…
In a recent paper Griffiths [38] has argued, based on the consistent histories interpretation, that Hilbert space quantum mechanics (QM) is noncontextual. According to Griffiths the problem of contextuality disappears if the apparatus is "designed and operated by a competent experimentalist" and we accept the Single Framework Rule (SFR). We will argue from a representational realist stance that the conclusion is incorrect due to the misleading understanding provided by Griffiths to the meaning of quantum contextuality and its relation to physical reality and measurements. We will discuss how t…
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible mappings from the position operators q_i and their quantum canonical operators p_i of a canonical theory, onto the discrete, commuting operators Q_i and P_i. In this paper we are particularly interested in harmonic oscillators. In the discrete system, these turn into deterministic models, which is our motivation for this study. We regard the procedure worked o…
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement-disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post- selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of contextuality. This proof is obtained by considering…
We present a discussion of the extended Wigner's friend thought experiment proposed by Frauchiger and Renner in [1]. We show by using various arguments, including textbook quantum mechanics and the ontological approach of Contexts, Systems, Modalities (CSM), that no contradiction arises if one admits that agents must agree on what is considered as a system and what is not. In such a contextually objective approach of quantum mechanics, the apparent contradiction is automatically removed. We also discuss why this mutual agreement between agents is already implicit in the standard formulations o…
Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of t…
Why microscopic objects exhibit wave properties (are delocalized), but macroscopic do not (are localized)? Traditional quantum mechanics attributes wave properties to all objects. When complemented with a deterministic collapse model (Quantum Stud.: Math. Found. 3, 279 (2016)) quantum mechanics can dissolve the discrepancy. Collapse in this model means contraction and occurs when the object gets in touch with other objects and satisfies a certain criterion. One single collapse usually does not suffice for localization. But the object rapidly gets in touch with other objects in a short time, le…
Weak value measurements have recently given rise to a large interest for both the possibility of measurement amplification and the chance of further quantum mechanics foundations investigation. In particular, a question emerged about weak values being proof of the incompatibility between Quantum Mechanics and Non-Contextual Hidden Variables Theories (NCHVT). A test to provide a conclusive answer to this question was given in [M. Pusey, Phys. Rev. Lett. 113, 200401 (2014)], where a theorem was derived showing the NCHVT incompatibility with the observation of anomalous weak values under specific…
Graph structure of quantum mechanics
针对量子力学的语境相关性问题，提出基于部分布尔代数的图结构方法，证明有限维量子系统由原子决定并推广到无限维，为量子语境相关性提供精确数学框架，揭示其为隐变量理论的图结构组合。
Relational Quantum Mechanics and Contextuality
该研究探讨关系量子力学中的稳定事实问题，提出可将一致历史形式体系的数学框架纳入关系量子力学，同时明确二者诠释差异，并讨论了狭义相对论与关系量子力学的异同及跨视角链接修正方案。
It is known that "quantum non locality", leading to the violation of Bell's inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, that we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing to make contextual inferences, which can in turn explain why quantum non locality does not contradict relativistic causality. But if the usual quantum state $ψ$ is predictively incomplete, how to complete it ? We give here a set of new …
We present a formal theory of contextuality for a set of random variables grouped into different subsets (contexts) corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly distributed, but across different contexts they are stochastically unrelated. The theory of contextuality is based on the analysis of the extent to which some of these random variables can be viewed as preserving their identity across different contexts when one considers all possible joint distributions imposed on the entire set of the random variables. We illustrat…
The no-signaling principle in quantum mechanics is shown to be a consequence of Gleason non-contextuality and the tensor product structure.
The Contextual Modal Logic of a Wigner's Friend Generalization
本文通过考虑量子系统的情境性，反驳了弗拉乌奇格-伦纳思想实验中所提出的量子力学逻辑不一致性的矛盾。
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation has all distinguishing features of the quantum model. Thus in spite all ``No-Go'' theorems (e.g., von Neumann, Kochen and Specker,..., Bell) we found the realist basis for quantum mechanics. Our representation is not standard model with hidden variables. In particular, this is not a reduction of quantum model to the classical one. Moreover, we see that such a …
We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong sequential-transformation contextuality is necessary and sufficient for deterministic computation of non-linear functions if classical components are restricted to mod2-linearity and matching constraints apply to any underlying ontology. For probabilistic computation, sequential-transformation contextuality is necessary and sufficient for advantage in this t…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including but not reducible to what other measurements are made "together" with the given one. We propose in this paper that the quantum observables generating these random variables be labeled contextually as well, making the sets of the observables in different contexts disjoint. A quantum observable is defined as a pair consisting of the observable's label and a sel…
In this chapter, we review a principled way of defining and measuring contextuality in systems with deterministic inputs and random outputs, recently proposed and developed in \citep{KujalaDzhafarovLarsson2015,DKL2015FooP}.
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the equations to be considered. Special attention is given to the notion of 'locality'. Various examples are worked out, followed by a systematic procedure to generate classical evolution laws and quantum Hamiltonians that are exactly equivalent. What is new here is that we consider interactions, keeping them as general as we can. The quantum systems found, form a de…
We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting observables on the same prepared state. While in the standard theory the measurement outcomes are uncorrelated, in a super-deterministic hidden variables theory the measurements would be correlated. We estimate that for macroscopic experiments the correlation time is too short to have been noticed yet, but that it may be possible with a suitably designed microscopic experiment to reach a parameter range where one would expect a super-deterministic modification of…
While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical reality--has emerged as a promising hypothesis. Magic states are quantum resources critical for practically achieving universal quantum computation. They exhibit the standard form of contextuality that is known to enable probabilistic advantages in a variety of computational and communicational tasks. Strong contextuality is an extremal form of contextuality desc…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one migh…
In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about --rather than as problems that need to be bypassed in order to allow a restoration of a classical "common sense" understanding of what there is. In particular, we discuss a solution to Kochen-Specker contextuality through the generalization of the meaning of global valuation. This i…
Deterministic Mechanical Wigner Negativity via Nonlinear Cavity Quantum Optomechanics in the Unresolved-Sideband Regime
本文提出利用腔响应对机械位置的非线性，在未分辨边带区无需单光子强耦合、额外非线性或条件测量即可确定性制备机械维格纳负性，并证明其在连续驱动稳态下持续存在。
Recently, an interesting form of non-classical effect which can be considered as a form of contextuality within quantum mechanics, has been demonstrated for a four-level system by discriminating the different routes that are taken for measuring a single observable. In this paper, we provide a simpler version of that proof for a single qutrit, which is also within the formalism of quantum mechanics and without recourse to any realist hidden variable model. The degeneracy of the eigenvalues and the L$\ddot{u}$der projection rule play important role in our proof.
Contextuality lays at the heart of quantum mechanics. In the prevailing opinion it is considered as a signature of 'quantumness' that classical theories lack. However, this assertion is only partially justified. Although contextuality is certainly true of quantum mechanics, it cannot be taken by itself as discriminating against classical theories. Here we consider a representative example of contextual behaviour, the so-called Mermin-Peres square, and present a discrete toy model of a bipartite system which reproduces the pattern of quantum predictions that leads to contradiction with the assu…
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually tak…
I argue that Bohmian mechanics (or any similar pilot-wave theory) cannot reasonably be claimed to be a deterministic theory. If one assumes the "quantum equilibrium distribution" provided by the wave function of the universe, Bohmian mechanics requires an external random oracle in order to describe the (Kolmogorov-Levin-Chaitin) algorithmic randomness properties of typical outcome sequences of long runs of repeated identical experiments (which provably follow from the Born rule). This oracle lies beyond the scope of Bohmian mechanics (or any deterministic extension thereof), including the impo…
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