Interplay among entanglement, measurement incompatibility, and nonlocality
arXiv:2303.08407 · doi:10.1088/2058-9565/ad5aba
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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