Optimal Bell inequalities for qubit-qudit systems

• URL: http://arxiv.org/abs/2404.02092v3
• Date: Wed, 04 Dec 2024 13:36:21 GMT
• Title: Optimal Bell inequalities for qubit-qudit systems
• Authors: Alexander Bernal, J. Alberto Casas, Jesus M. Moreno,
• Abstract summary: We evaluate the maximal Bell violation for a generic qubit-qudit system. We show the impossibility of improving the amount of Bell-violation by embedding the qudit in a Hilbert space of larger dimension.
• Score: 44.99833362998488
• License:
• Abstract: We evaluate the maximal Bell violation for a generic qubit-qudit system, obtaining easily computable expressions in arbitrary qudit dimension. This work generalizes the well-known Horodeckis's result for a qubit-qubit system. We also give simple lower and upper bounds on that violation. We apply our general results to address a number of issues. Namely, we obtain a bound on the degree of purity required in a system to exhibit nonlocality and study the statistics of nonlocality in random density matrices. Besides, we show the impossibility of improving the amount of Bell-violation by embedding the qudit in a Hilbert space of larger dimension. We also discuss how the results are generalized to POVM measurements. Finally, the general result is illustrated with a family of density matrices in the context of a qubit-qutrit system.

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