Recent advances in contextuality tests

Our everyday experiences support the hypothesis that physical systems exist independently of the act of observation. Concordant theories are characterized by the objective realism assumption whereby the act of measurement simply reveals preexisting well defined elements of reality. In stark contrast quantum mechanics portrays a world in which reality loses its objectivity and is in fact created by observation. Quantum contextuality as first discovered by Bell [Rev. Mod. Phys. 38, 447 (1966)] and Kochen-Specker [J. Math. Mech. 17, 59 (1967)] captures aspects of this philosophical clash between classical and quantum descriptions of the world. Here we briefly summarize some of the more recent advances in the field of quantum contextuality. We approach quantum contextuality through its close relation to Bell type nonlocal scenarios and highlight some of the rapidly developing tests and experimental implementations.Comment: 45 pages, 8 figure

Simple method for experimentally testing any form of quantum contextuality

Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of performing sequences of projective measurements on individual quantum systems. Here we show that two-point correlations between binary compatible observables are sufficient to reveal any form of contextuality. This allows us to design simple experiments that are more robust against imperfections and easier to analyze, thus opening the door for observing interesting forms of contextuality, including those requiring quantum systems of high dimensions. In addition, it allows us to connect contextuality to communication complexity scenarios and reformulate a recent result relating contextuality and quantum computation.Comment: REVTeX4, 6 pages, 2 figure

What does an experimental test of quantum contextuality prove or disprove?

The possibility to test experimentally the Bell-Kochen-Specker theorem is investigated critically, following the demonstrations by Meyer, Kent and Clifton-Kent that the predictions of quantum mechanics are indistinguishable (up to arbitrary precision) from those of a non-contextual model, and the subsequent debate to which extent these models are actually classical or non-contextual. The present analysis starts from a careful consideration these "finite-precision" approximations. A stronger condition for non-contextual models, dubbed , is exhibited. It is shown that it allows to formulate approximately the constraints in Bell-Kochen-Specker theorems such as to render the usual proofs robust. As a consequence, one can experimentally test to finite precision ontologically faithful non-contextuality, and thus experimentally refute explanations from this smaller class. We include a discussion of the relation of ontological faithfulness to other proposals to overcome the finite precision objection.Comment: REVTEX4, 9 pages, 57 references; corrected example 7 in v2. To appear in Journal of Physics A, special issue "50 years of Bell's theorem

Logical and inequality based contextuality for qudits

In this work we present a generalization of the recently developed Hardy-like logical proof of contextuality and of the so-called KCBS contextuality inequality for any qudit of dimension greater than three. Our approach uses compatibility graphs that can only be satisfied by qudits. We find a construction for states and measurements that satisfy these graphs and demonstrate both logical and inequality based contextuality for qudits. Interestingly, the quantum violation of the inequality is constant as dimension increases. We also discuss the issue of imprecision in experimental implementations of contextuality tests and a way of addressing this problem using the notion of ontological faithfulness

A Logical Proof of Quantum Correlations Requiring Entanglement Measurements

We present a logical type of proof of contextuality for a two-qubit state. We formulate a paradox that cannot be verified by a two-qubit system with local measurements while it is possible by using entanglement measurements. With our scheme we achieve $p_{\rm Hardy} \approx 0.167$, which is the highest probability obtained for a system of similar dimension. Our approach uses graph theory and the global exclusivity principle to give an interpretation of logical type of proofs of quantum correlations. We review the Hardy paradox and find connection to the KCBS inequality. We apply the same method to build a paradox based the CHSH inequality

Contextuality supplies the magic for quantum computation

Quantum computers promise dramatic advantages over their classical counterparts, but the answer to the most basic question "What is the source of the power in quantum computing?" has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via magic state distillation. This is a conceptually satisfying link because contextuality provides one of the fundamental characterizations of uniquely quantum phenomena and, moreover, magic state distillation is the leading model for experimentally realizing fault-tolerant quantum computation. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the nonlocality of quantum theory is a particular kind of contextuality and nonlocality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation and bounding the overhead cost for the classical simulation of quantum algorithms.Comment: 5+4 pages, 2 figure

All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences

Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of which has a finite number of outcomes. Given any fixed sets of operational equivalences among the preparations and among the measurements as input, the algorithm returns a set of noncontextuality inequalities whose satisfaction is necessary and sufficient for a set of operational data to admit of a noncontextual model. Additionally, we show that the space of noncontextual data tables always defines a polytope. Finally, we provide a computationally efficient means for testing whether any set of numerical data admits of a noncontextual model, with respect to any fixed operational equivalences. Together, these techniques provide complete methods for characterizing arbitrary noncontextuality scenarios, both in theory and in practice. Because a quantum prepare-and-measure experiment admits of a noncontextual model if and only if it admits of a positive quasiprobability representation, our techniques also determine the necessary and sufficient conditions for the existence of such a representation.Comment: 11 page

Classical systems can be contextual too: Analogue of the Mermin-Peres square

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 assumption of non-contextuality. This illustrates that quantum-like contextual effects have their analogues within classical models with epistemic constraints such as limited information gain and measurement disturbance.Comment: 16 pages, 7 figures. Final version as published in Annals of Physic

Negative Probabilities and Contextuality

There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is contextuality-by-default, put forth by Dzhafarov and Kujala. The goal of this paper is to present a tutorial on a different approach: negative probabilities. We do so by presenting the overall theory of negative probabilities in a way that is consistent with contextuality-by-default and by examining with this theory some simple examples where contextuality appears, both in physics and psychology.Comment: 28 pages, 5 figure

Weak Interaction Processes: Which Quantum Information is revealed?

We analyze the achievable limits of the quantum information processing of the weak interaction revealed by hyperons with spin. We find that the weak decay process corresponds to an interferometric device with a fixed visibility and fixed phase difference for each hyperon. Nature chooses rather low visibilities expressing a preference to parity conserving or violating processes (except for the decay $\Sigma^+\longrightarrow p \pi^0$). The decay process can be considered as an open quantum channel that carries the information of the hyperon spin to the angular distribution of the momentum of the daughter particles. We find a simple geometrical information theoretic interpretation of this process: two quantization axes are chosen spontaneously with probabilities $\frac{1\pm\alpha}{2}$ where $\alpha$ is proportional to the visibility times the real part of the phase shift. Differently stated the weak interaction process corresponds to spin measurements with an imperfect Stern-Gerlach apparatus. Equipped with this information theoretic insight we show how entanglement can be measured in these systems and why Bell's nonlocality (in contradiction to common misconception in literature) cannot be revealed in hyperon decays. We study also under which circumstances contextuality can be revealed.Comment: 7 pages, 3 figures, version 2: title changed, minor revisio