Violation of Bell-CHSH inequalities through optimal local filters in the vacuum

TL;DR

This paper explores how local filtering operations can reveal Bell-CHSH inequality violations in entangled qubits initially uncorrelated but interacting with a vacuum scalar field, highlighting a trade-off between success probability and violation region.

Contribution

It constructs optimal local filtering operations and derives success probabilities, demonstrating how to reliably detect Bell-CHSH violations in this quantum field scenario.

Findings

Optimal filtering operations enhance Bell-CHSH violation detection.

Success probability relates to the size of violation parameter region.

Trade-off identified between success probability and violation region size.

Abstract

We investigate quantum correlations appearing for two qubit detectors which are initially uncorrelated and locally coupled to a massless scalar field in a vacuum state. Under the perturbation up to the second order in the coupling, the state of the detectors can be entangled through the interaction with the scalar field but satisfies the Bell-CHSH inequality. The violation of the Bell-CHSH inequality for such an entangled state is revealed by local filtering operations. In this paper, we construct the optimal filtering operations for the qubit detectors and derive the success probability of the filtering. The success probability characterizes the reliability of revealing the violation of the Bell-CHSH inequality by the filtering operations. Through these analyses, we demonstrate a trade-off relation between the success probability and the size of parameter region showing the violation of the Bell-CHSH inequality.