Minimal scenario facet Bell inequalities for multi-qubit states
- URL: http://arxiv.org/abs/1809.05727v2
- Date: Fri, 17 Mar 2023 16:17:11 GMT
- Title: Minimal scenario facet Bell inequalities for multi-qubit states
- Authors: Arpan Das, Chandan Datta and Pankaj Agrawal
- Abstract summary: Facet inequalities play an important role in detecting the nonlocality of a quantum state.
With the increase in the number of parties, measurement outcomes, or/and the number of measurement settings, there are more nontrivial facet inequalities.
We show that for noisy W states, our inequality is more effective than the well-known Mermin inequality.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Facet inequalities play an important role in detecting the nonlocality of a
quantum state. The number of such inequalities depends on the Bell test
scenario. With the increase in the number of parties, measurement outcomes,
or/and the number of measurement settings, there are more nontrivial facet
inequalities. For several Bell scenarios, by involving two dichotomic
measurement settings for two parties and one dichotomic measurement by other
parties, we show that the local polytope has only one nontrivial facet. For
three parties, we have three variants of this inequality, depending upon which
party is doing one dichotomic measurement. This measurement scenario for a
multipartite state may be considered as the minimal scenario involving
multipartite correlations that can detect nonlocality. We show that this
inequality is violated by all generalized GHZ states. Being the only facet Bell
inequality, this inequality is also violated by any entangled three-qubit pure
state. We also show that for noisy W states, our inequality is more effective
than the well-known Mermin inequality.
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