Testing of quantum nonlocal correlations under constrained free will and imperfect detectors

TL;DR

This paper investigates the robustness of quantum nonlocal correlations under limited free will and imperfect detectors, establishing thresholds for detector efficiency and dark counts to reliably certify nonlocality.

Contribution

It introduces a framework for analyzing quantum nonlocality with constrained free will and imperfect detectors, including new LRHV inequalities and threshold criteria.

Findings

Derived threshold values for detector efficiency and dark counts.

Proposed new LRHV inequalities with constrained free will.

Analyzed robustness of nonlocality tests under practical imperfections.

Abstract

In this work, we deal with the relaxation of two central assumptions in standard locally realistic hidden variable (LRHV) inequalities: free will in choosing measurement settings, and the presence of perfect detectors at the measurement devices. Quantum correlations violating LRHV inequalities are called quantum nonlocal correlations. In principle, in an adversarial situation, there could be a hidden variable introducing bias in the selection of measurement settings, but observers with no access to that hidden variable could be unaware of the bias. In practice, however, detectors do not have perfect efficiency. A main focus of this paper is the introduction of the framework in which given a quantum state with nonlocal behavior under constrained free will, we can determine the threshold values of detector parameters (detector inefficiency and dark counts) such that the detectors are robust enough to certify nonlocality. We also introduce a class of LRHV inequalities with constrained free will, and we discuss their implications in the testing of quantum nonlocal correlations.