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

Bell nonlocality with intensity information only

We address the problem of detecting bipartite Bell nonlocality whenever the only experimental information are the intensities produced in each run of the experiment by an unknown number of particles. We point out that this scenario naturally occurs in Bell experiments with parametric down-conversion when the crystal is pumped by strong pulses, in Bell tests with distant sources and in which particles suffer different delays during their flight, in Bell experiments using living cells as photo detectors, and in Bell experiments where the pairing information is physically removed. We show that, although Bell nonlocality decreases as the number of particles increases, if the parties can distinguish arbitrarily small differences of intensities and the visibility is larger than $0.98$, then Bell nonlocality can still be experimentally detected with fluxes of up to $15$ particles. We show that this prediction can be tested with current equipment in a Bell experiment where pairing information is physically removed, but requires the assumption of fair sampling.Comment: 7 pages, 2 figure

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

Reply to Marinatto's comment on "Bell's theorem without inequalities and without alignments"

Marinatto claims that in the proof of Bell's theorem without inequalities and without alignments [A. Cabello, Phys. Rev. Lett. 91, 230403 (2003)], local observables cannot be measured by means of tests on individual qubits. Marinatto's claim is incorrect. To support this, the proof is explicitly rewritten in terms of tests on individual qubits.Comment: REVTeX4, 1 pag

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.