Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities

Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While various proofs of such contextual behavior of quantum systems have been established, relatively little is known concerning the possibility to demonstrate this intriguing feature for indistinguishable particles. Here, we show in a simple and systematic manner that with projective measurements alone, it is possible to demonstrate quantum contextuality for such systems of arbitrary Hilbert space dimensions, including those corresponding to a qubit. Our demonstration is applicable to a single fermion as well as multiple fermions, and thus also a composite boson formed from an even number of fermions. In addition, our approach gives a clear demonstration of the intimate connection between complementarity and contextuality, two seemingly unrelated aspects of quantum theory.Comment: 9 pages, no figure; Major changes; More changes. Accepted in Scientific Report

Commutativity, comeasurability, and contextuality in the Kochen-Specker arguments

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 represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting (ii) associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality.Comment: 27 pages, 1 figur

Noncontextuality, Finite Precision Measurement and the Kochen-Specker Theorem

Meyer recently queried whether non-contextual hidden variable models can, despite the Kochen-Specker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental precision. Clifton and Kent have presented constructions of non-contextual hidden variable theories which, they argued, indeed simulate quantum mechanics in this way. These arguments have evoked some controversy. One aim of this paper is to respond to and rebut criticisms of the MCK papers. We thus elaborate in a little more detail how the CK models can reproduce the predictions of quantum mechanics to arbitrary precision. We analyse in more detail the relationship between classicality, finite precision measurement and contextuality, and defend the claims that the CK models are both essentially classical and non-contextual. We also examine in more detail the senses in which a theory can be said to be contextual or non-contextual, and in which an experiment can be said to provide evidence on the point. In particular, we criticise the suggestion that a decisive experimental verification of contextuality is possible, arguing that the idea rests on a conceptual confusion.Comment: 27 pages; published version; minor changes from previous versio

Bell non-locality and Kochen-Specker contextuality: How are they connected?

Bell non-locality and Kochen-Specker (KS) contextuality are logically independent concepts, fuel different protocols with quantum vs classical advantage, and have distinct classical simulation costs. A natural question is what are the relations between these concepts, advantages, and costs. To address this question, it is useful to have a map that captures all the connections between Bell non-locality and KS contextuality in quantum theory. The aim of this work is to introduce such a map. After defining the theory-independent notions of Bell non-locality and KS contextuality for ideal measurements, we show that, in quantum theory, due to Neumark's dilation theorem, every matrix of quantum Bell non-local correlations can be mapped to an identical matrix of KS contextual correlations produced in a scenario with identical relations of compatibility but where measurements are ideal and no space-like separation is required. A more difficult problem is identifying connections in the opposite direction. We show that there are "one-to-one" and partial connections between KS contextual correlations and Bell non-local correlations for some KS contextuality scenarios, but not for all of them. However, there is also a method that transforms any matrix of KS contextual correlations for quantum systems of dimension $d$ into a matrix of Bell non-local correlations between two quantum subsystems each of them of dimension $d$. We collect all these connections in map and list some problems which can benefit from this map.Comment: 13 pages, 2 figure

Pre- and post-selection, weak values, and contextuality

By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of pre-and-post-selection (PPS), it is possible to assign definite values to observables in a new and surprising way. Physical reasons are presented for restrictions on these assignments. When measurements are performed which do not disturb the pre- and post-selection (i.e. weak measurements), then novel experimental aspects of contextuality can be demonstrated including a proof that every PPS-paradox with definite predictions implies contextuality. Certain results of these measurements (eccentric weak values with e.g. negative values outside the spectrum), however, cannot be explained by a "classical-like" hidden variable theory.Comment: Identical content; stream-lined verbal presentatio