Kochen-Specker theorem and experimental test on hidden variables

A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett. 80, 1797 (1998)] is shown to be related with the smallest proof of the Kochen-Specker theorem currently known [Phys. Lett. A 212, 183 (1996)]. This proof contains eighteen yes-no questions about a four-dimensional physical system, combined in nine mutually incompatible tests. When these tests are considered as tests about a two-part two-state system, then quantum mechanics and non-contextual hidden variables make the same predictions for eight of them, but make different predictions for the ninth. Therefore, this ninth test would allow us to discriminate between quantum mechanics and noncontextual hidden-variable theories in a (gedanken) single run experiment.Comment: 4 pages, 1 figure. To appear in Int. J. Mod. Phys.

Alice and Bob get away with it: A playlet

Alice and Bob use Aravind's version of the Bell-Kochen-Specker theorem to fend off awkward questions about what exactly they were doing in Amsterdam last week

Proposed test of macroscopic quantum contextuality

We show that, for any system with a number of levels which can be identified with n qubits, there is an inequality for the correlations between three compatible dichotomic measurements which must be satisfied by any noncontextual theory, but is violated by any quantum state. Remarkably, the violation grows exponentially with n, and the tolerated error per correlation also increases with n, showing that state-independent quantum contextuality is experimentally observable in complex systems.Comment: REVTeX4, 5 pages, 1 figur

Kochen-Specker theorem as a precondition for secure quantum key distribution

We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each QKD protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory.Comment: 4 pages, To appear in Phys. Rev.

Quantum contextuality in N-boson systems

Quantum contextuality in systems of identical bosonic particles is explicitly exhibited via the maximum violation of a suitable inequality of Clauser-Horne-Shimony-Holt type. Unlike the approaches considered so far, which make use of single-particle observables, our analysis involves collective observables constructed using multi-boson operators. An exemplifying scheme to test this violation with a quantum optical setup is also discussed.Comment: 4 pages, 1 figure, LaTe

Twin inequality for fully contextual quantum correlations

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 contextual quantum correlations.Comment: REVTeX4, 4 pages, 1 figur

An entropic approach to local realism and noncontextuality

For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality) inequalities. In this paper we explore this entropic approach and derive tight entropic inequalities for various scenarios. One advantage of entropic inequalities is that they easily adapt to situations like bilocality scenarios, which have additional independence requirements that are non-linear on the level of probabilities, but linear on the level of entropies. Another advantage is that, despite the nonlinearity, taking detection inefficiencies into account turns out to be very simple. When joint measurements are conducted by a single detector only, the detector efficiency for witnessing quantum contextuality can be arbitrarily low.Comment: 12 pages, 8 figures, minor mistakes correcte

A Bayesian Analogue of Gleason's Theorem

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published versio

Is there contextuality for a single qubit?

It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)], that the Kochen-Specker theorem applies to two dimensions if one uses Positive Operator-Valued Measures. We show that contextuality in their models is not of the Kochen-Specker type. It is rather the result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between POVM elements and projectors on the extended Hilbert space and the same POVM element has to originate from two different projectors when used in Cabello's and Nakamura's models. Moreover, we propose a hidden-variable formulation of the above models.Comment: 4 pages, 1 figure, comments welcom

Simulating Quantum Mechanics by Non-Contextual Hidden Variables

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 variable model. We show here by explicit construction that there are indeed such non-contextual hidden variable models, both for projection valued and positive operator valued measurements.Comment: 15 pages. Journal version. Only minor typo corrections from last versio