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Optics Express

Experimental demonstration of hidden nonlocality with local filters

Yang Wang, Jian Li, Xiao-Run Wang, Tongjun Liu, Qin Wang

Published Apr 14, 2020• 10 citations
Publisher

Abstract

The violation of the Bell inequalities implies that quantum mechanics cannot be interpreted using any local hidden variable theory. However, particular quantum states that can originally be described using a local hidden variable model surprisingly exhibit nonlocality by employing local filters before a standard Bell test is performed. This is referred to as hidden nonlocality. In this study, we provide the experimental demonstration of hidden nonlocality through linear optics towards the local states which are put forword by Hirsch et al., PRL 111, 160402 (2013). A class of local states is generated through a spontaneous parametric down-conversion process, and the violation of the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality is observed by applying local filters. Our experimental results confirm the superiority of local filters, and throw light on deep understanding the intriguing phenomena of hidden nonlocality and local states.

DOI
10.1364/oe.387568

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The violation of the Bell inequalities implies that quantum mechanics cannot be interpreted using any local hidden variable theory. However, particular quantum states that can originally be described using a local hidden variable model surprisingly exhibit nonlocality by employing local filters before a standard Bell test is performed. This is referred to as hidden nonlocality. In this study, we provide the experimental demonstration of hidden nonlocality through linear optics towards the local states which are put forword by Hirsch et al., PRL 111, 160402 (2013). A class of local states is generated through a spontaneous parametric down-conversion process, and the violation of the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality is observed by applying local filters. Our experimental results confirm the superiority of local filters, and throw light on deep understanding the intriguing phenomena of hidden nonlocality and local states.
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.
This Master's thesis has two central subjects: the simulation of correlations generated by local measurements on entangled quantum states by local hidden-variables models and the revelation of hidden nonlocality. We present and detail the Werner's local model and the hidden nonlocality of some Werner states of dimension d≥5d\geq5d≥5, the Gisin-Degorre's local model for a Werner state of dimension d=2d=2d=2 and the local model of Hirsch et al. for mixtures of the singlet state and noise, all of them for projective measurements. Finally, we introduce the local model for POVMs of Hirsch et al. for a state constructed upon the singlet with noise, that still violates the CHSH inequality after local filters are applied, hence presenting the so-called genuine hidden nonlocality.
The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely, projective measurements. Here, we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements, and show that the states violate a Bell inequality after local filtering. Hence, there exist entangled states, the nonlocality of which can be revealed only by using a sequence of measurements. Finally, we show that genuine hidden nonlocality can be maximal. There exist entangled states for which a sequence of measurements can lead to maximal violation of a Bell inequality, while the statistics of nonsequential measurements is always local.
We describe an experimental test of local realistic and nonlocal realistic theories using polarization-entangled two-photon singlet states created using a fiber-based polarization Sagnac interferometer. We show a violation of Bell's inequality in the Clauser-Horne-Shimony-Holt form by 15 standard deviations, thus excluding local hidden-variable theories, and a violation of a Leggett-type nonlocal hidden-variable inequality by more than three standard deviations, thus excluding a class of nonlocal hidden-variable theories.
The Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, which is proven in the context of the local hidden-variable theory, has been used as a test to reveal the failure of the hidden-variable theory and to prove the validity of the quantum theory. We note that the violation of the BCHSH inequality is caused by the noncommutativity of quantum observables and find a systematic method of constructing generalizations of the BCHSH inequality. This method is used to invent a new quantity, which is defined in a two-qubit system and satisfies a new type of inequality. This provides a fair test of the quantum theory. Remaining problems are also discussed.