Interplay among entanglement, measurement incompatibility, and nonlocality

• URL: http://arxiv.org/abs/2303.08407v2
• Date: Fri, 20 Jun 2025 07:54:39 GMT
• Title: Interplay among entanglement, measurement incompatibility, and nonlocality
• Authors: Yuwei Zhu, Xingjian Zhang, Xiongfeng Ma,
• Abstract summary: Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system.<n>We quantify entanglement using a family of generalized Clauser-Horne-Shimony-Holt-type Bell inequalities.<n>We show that one can utilize the nonlocal statistics by optimizing the Bell inequality for better entanglement estimation.
• Score: 2.926688732713416
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system. A natural question is how much entanglement is required for a given nonlocal behavior. Here, we explore this question by quantifying entanglement using a family of generalized Clauser-Horne-Shimony-Holt-type Bell inequalities. Given a Bell-inequality violation, we derive analytical lower bounds on the entanglement of formation, a measure related to entanglement dilution. The bounds also lead to an analytical estimation of the negativity of entanglement. In addition, we consider one-way distillable entanglement tied to entanglement distillation and derive tight numerical estimates. With the additional assumptions of qubit-qubit systems, we find that the relationship between entanglement and measurement incompatibility is not simply a trade-off under a fixed nonlocal behavior. Furthermore, we apply our results to two realistic scenarios -- non-maximally entangled and Werner states. We show that one can utilize the nonlocal statistics by optimizing the Bell inequality for better entanglement estimation.

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