Finding optimal Bell inequalities using the cone-projection technique

• URL: http://arxiv.org/abs/2103.17247v1
• Date: Wed, 31 Mar 2021 17:50:43 GMT
• Title: Finding optimal Bell inequalities using the cone-projection technique
• Authors: Fabian Bernards and Otfried G\"uhne
• Abstract summary: cone-projection technique developed to find optimal Bell inequalities under some constraints. We use the method to generalize the I4422 inequality to three particles and a so-called GYNI inequality to four particles. We discuss the obtained inequalities in some detail and characterize their violation in quantum mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to find all optimal Bell inequalities under some constraints, which may be given by some symmetry or other linear conditions. In this paper we extend this work in several directions. We use the method to generalize the I4422 inequality to three particles and a so-called GYNI inequality to four particles. Additionally, we find Bell inequalities for three particles that generalize the I3322 inequality and the CHSH inequality at the same time. We discuss the obtained inequalities in some detail and characterize their violation in quantum mechanics.

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