Coarse-grained self-testing
- URL: http://arxiv.org/abs/2103.11680v3
- Date: Tue, 14 Dec 2021 17:21:13 GMT
- Title: Coarse-grained self-testing
- Authors: Ir\'en\'ee Fr\'erot and Antonio Ac\'in
- Abstract summary: We show how a coarse-grained version of self-testing is possible in which physically relevant properties of a many-body system are certified.
We prove that a many-body generalization of the chained Bell inequality is maximally violated if and only if the underlying quantum state is equal, up to local isometries, to a many-body singlet.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Self-testing is a device-independent method that usually amounts to show that
the maximal quantum violation of a Bell's inequality certifies a unique quantum
state, up to some symmetries inherent to the device-independent framework. In
this work, we enlarge this approach and show how a coarse-grained version of
self-testing is possible in which physically relevant properties of a many-body
system are certified. For that we study a Bell scenario consisting of an
arbitrary number of parties and show that the membership to a set of
(entangled) quantum states whose size grows exponentially with the number of
particles can be self-tested. Specifically, we prove that a many-body
generalization of the chained Bell inequality is maximally violated if and only
if the underlying quantum state is equal, up to local isometries, to a
many-body singlet. The maximal violation of the inequality therefore certifies
any statistical mixture of the exponentially-many orthogonal pures states
spanning the singlet manifold.
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