Possibilistic approach to network nonlocality
- URL: http://arxiv.org/abs/2208.13526v2
- Date: Tue, 20 Sep 2022 12:33:45 GMT
- Title: Possibilistic approach to network nonlocality
- Authors: Antoine Restivo, Nicolas Brunner, Denis Rosset
- Abstract summary: We explore a possibilistic approach, where only patterns of possible outcomes matter, and apply it to Bell nonlocality in networks with independent sources.
We present various algorithms for determining whether a given outcome pattern can be achieved via classical resources or via non-signaling resources.
We show how to construct certificates for detecting the nonlocality of a certain pattern, in the form of nonlinear Bell-type inequalities involving joint probabilities.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The investigation of Bell nonlocality traditionally relies on joint
probabilities of observing certain measurement outcomes. In this work we
explore a possibilistic approach, where only patterns of possible outcomes
matter, and apply it to Bell nonlocality in networks with independent sources.
We present various algorithms for determining whether a given outcome pattern
can be achieved via classical resources or via non-signaling resources. Next we
illustrate these methods considering the triangle and square networks (with
binary outputs and no inputs), identifying patterns that are incompatible with
the network structure, as well as patterns that imply nonlocality. In
particular, we obtain an example of quantum nonlocality in the square network
with binary outcomes. Moreover, we show how to construct certificates for
detecting the nonlocality of a certain pattern, in the form of nonlinear
Bell-type inequalities involving joint probabilities. Finally, we show that
these inequalities remain valid in the case where the sources in the network
become partially correlated.
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