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Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

1
Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan
2
NTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(2), 185; https://doi.org/10.3390/e21020185
Received: 15 December 2018 / Revised: 12 February 2019 / Accepted: 12 February 2019 / Published: 15 February 2019
(This article belongs to the Special Issue Quantum Nonlocality)
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Abstract

The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell’s seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method—initially developed for performing a hypothesis test of local-hidden-variable theories—can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test. View Full-Text
Keywords: quantum nonlocality; Bell test; device-independent; p-value; hypothesis testing; nonsignaling quantum nonlocality; Bell test; device-independent; p-value; hypothesis testing; nonsignaling
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Liang, Y.-C.; Zhang, Y. Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing. Entropy 2019, 21, 185.

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