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中国物理B：英文版

Minimum detection efficiency for the loophole-free confirmation of quantum contextuality

向阳, 洪方昱

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Klyachko–Can–Binicioglu–Shumovsky (KCBS) inequality is a Bell-like inequality,the violation of which can be used to confirm the existence of quantum contextuality.However,the imperfection of detection efficiency may cause the so-called loophole in actual KCBS’s experiments.We derive an alternative KCBS inequality to deal with the loophole in actual KCBS’s experiments.We prove that if the experimental data violate this KCBS inequality,the loophole-free violation of the original KCBS inequality will occur.We show that the minimum detection efficiency needed for a loophole-free violation of the KCBS inequality is about 0.9738.

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Klyachko–Can–Binicioglu–Shumovsky (KCBS) inequality is a Bell-like inequality,the violation of which can be used to confirm the existence of quantum contextuality.However,the imperfection of detection efficiency may cause the so-called loophole in actual KCBS’s experiments.We derive an alternative KCBS inequality to deal with the loophole in actual KCBS’s experiments.We prove that if the experimental data violate this KCBS inequality,the loophole-free violation of the original KCBS inequality will occur.We show that the minimum detection efficiency needed for a loophole-free violation of the KCBS inequality is about 0.9738.
Klyachko—Can—Binicioğlu—Shumovsky (KCBS) inequality is a Bell-like inequality, the violation of which can be used to confirm the existence of quantum contextuality. However, the imperfection of detection efficiency may cause the so-called loophole in actual KCBS's experiments. We derive an alternative KCBS inequality to deal with the loophole in actual KCBS's experiments. We prove that if the experimental data violate this KCBS inequality, the loophole-free violation of the original KCBS inequality will occur. We show that the minimum detection efficiency needed for a loophole-free violation of the KCBS inequality is about 0.9738.
We show that the maximum quantum violation of the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality is exactly the maximum value satisfying the following principle: The sum of probabilities of pairwise exclusive events cannot exceed 1. We call this principle "global exclusivity," since its power shows up when it is applied to global events resulting from enlarged scenarios in which the events in the inequality are considered jointly with other events. We identify scenarios in which this principle singles out quantum contextuality, and show that a recent proof excluding nonlocal boxes follows from the maximum violation imposed by this principle to the KCBS inequality.
Svetlichny's inequality (SI) is a Bell-like inequality, the violation of which can be used to confirm the existence of genuine multipartite correlations. However, poor detector efficiency can possibly cause a so-called detection loophole in actual Svetlichny experiments. We derive an alternative SI to deal with this loophole. If the experimental data can violate this SI, it must result in loophole-free violation of the original SI. We show that the minimum detection efficiency needed for a loophole-free violation of the tripartite SI is about 0.970.970.97. For the general case of nnn particles, we give the analytic expression of the needed detection efficiency, and find that its value monotonically and rapidly approaches 1 as the number of particles increases.
Klyachko, Can, Binicioğlu, and Shumovsky (KCBS) have introduced an inequality which holds if there is a noncontextual hidden variable theory. It is called KCBS inequality. Its violation shows a contradiction between predictions of quantum theory and noncontextual hidden variable theories. Bell-Kochen-Specker (BKS) theorem also shows that there are no noncontextual hidden variable theories in quantum theory by showing that there is no value assignment on a set of all observables. Thus, its approach is different from KCBS inequality. In the present paper, we show a logical relation between KCBS inequality and a value assignment, and examine a consequence of this logical relation.
The intrinsic unpredictability of measurements in quantum mechanics can be used to produce genuine randomness. Here, we demonstrate a random number generator where the randomness is certified by quantum contextuality in connection with the Kochen-Specker theorem. In particular, we generate random numbers from measurements on a single trapped ion with three internal levels, and certify the generated randomness by showing a bound on the minimum entropy through observation of violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Concerning the test of the KCBS inequality, we close the detection efficiency loophole for the first time and make it relatively immune to the compatibility loophole. In our experiment, we generate 1 × 10(5) random numbers that are guaranteed to have 5.2 × 10(4) bits of minimum entropy with a 99% confidence level.
Abstract The Clauser–Horne–Shimony-Holt (CHSH) inequality tests locality in quantum theory and is recognized as one of Bell’s inequalities. In contrast, the Klyachko–Can–Binicioğlu–Shumovsky (KCBS) inequality tests noncontextuality, which refers to the idea that measurement outcomes are determined by intrinsic properties independent of other measurements that could be performed simultaneously. While individual quantum states can violate these inequalities separately, it was believed that no single state could violate both simultaneously. This relationship suggests a trade-off between nonlocality and contextuality: if one is violated, the other cannot be. Such a relationship is known as a monogamy relation. Xue et al demonstrated, however, that simultaneous violations of both the CHSH and KCBS inequalities are possible with specific choices of observables. This finding challenges the universal validity of the monogamy relation. They further showed that numerous scenarios exist in which both the CHSH inequality and a noncontextuality inequality involving more than five observables are violated. Nevertheless, the number of such scenarios is finite. In this paper, we extend these findings in two significant ways. First, we show that infinitely many scenarios exist where both the CHSH inequality and a noncontextuality inequality involving an odd number of observables are violated. This demonstrates that the monogamy relation between the CHSH inequality and the noncontextuality inequality fails in infinitely many cases. Second, we identify quantum states that violate both the KCBS inequality and a locality inequality distinct from the CHSH inequality. Our results highlight that the so-called ‘monogamy relation’ between nonlocality and contextuality is not universally valid. Instead, it appears that both phenomena can coexist under broader conditions than initially expected, thus challenging the conventional viewpoint and paving the way for new theoretical and experimental research.