Quantum Bell inequalities from Information Causality -- tight for
Macroscopic Locality
- URL: http://arxiv.org/abs/2103.05029v3
- Date: Wed, 18 May 2022 13:22:46 GMT
- Title: Quantum Bell inequalities from Information Causality -- tight for
Macroscopic Locality
- Authors: Mariami Gachechiladze, Bart{\l}omiej B\k{a}k, Marcin Paw{\l}owski, and
Nikolai Miklin
- Abstract summary: In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities.
We present a family of inequalities, which approximate the set of quantum correlations in Bell scenarios where the number of settings or outcomes can be arbitrary.
- Score: 0.34771439623170125
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In a Bell test, the set of observed probability distributions complying with
the principle of local realism is fully characterized by Bell inequalities.
Quantum theory allows for a violation of these inequalities, which is famously
regarded as Bell nonlocality. However, finding the maximal degree of this
violation is, in general, an undecidable problem. Consequently, no algorithm
can be used to derive quantum analogs of Bell inequalities, which would
characterize the set of probability distributions allowed by quantum theory.
Here we present a family of inequalities, which approximate the set of quantum
correlations in Bell scenarios where the number of settings or outcomes can be
arbitrary. We derive these inequalities from the principle of Information
Causality, and thus, we do not assume the formalism of quantum mechanics.
Moreover, we identify a subspace in the correlation space for which the derived
inequalities give the necessary and sufficient conditions for the principle of
Macroscopic Locality. As a result, we show that in this subspace, the principle
of Information Causality is strictly stronger than the principle of Macroscopic
Locality.
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