Interplay of Quantum Resources in Nonlocality Tests

TL;DR

This study experimentally investigates how quantum resources like entanglement and measurement incompatibility interact to influence nonlocality, achieving loophole-free Bell violation and revealing complex relationships among these resources for quantum information tasks.

Contribution

The paper provides the first high-efficiency, loophole-free Bell test using a generalized CHSH inequality and explores the nuanced interplay between nonlocality, entanglement, and measurement incompatibility.

Findings

Loophole-free Bell violation of 2.0132 achieved.

Device-independent entanglement lower bound of 0.0159.

Measurement incompatibility quantified with an effective overlap of 4.3883×10⁻⁵.

Abstract

Nonlocality, evidenced by the violation of Bell inequalities, not only signifies entanglement but also highlights measurement incompatibility in quantum systems. Utilizing the generalized Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, our high-efficiency optical setup achieves a loophole-free violation of $2.0132$. This result provides a device-independent lower bound on entanglement, quantified as the entanglement of formation at $0.0159$. Moreover, by tuning the parameters of the generalized Bell inequality, we enhance the estimation of measurement incompatibility, which is quantified by an effective overlap of $4.3883 \times 10^{-5}$. To explore the intricate interplay among nonlocality, entanglement, and measurement incompatibility, we generate mixed states, allowing for flexible modulation of entanglement via fast switching among the four Bell states using Pockels cells, achieving a fidelity above $99.10\%$. Intriguingly, our results reveal a counterintuitive relationship where increasing incompatibility initially boosts nonlocality but eventually leads to its reduction. Typically, maximal nonlocality does not coincide with maximal incompatibility. This experimental study sheds light on the optimal management of quantum resources for Bell-inequality-based quantum information processing.