More Nonlocality with Less Entanglement in CHSH Experiments using Inefficient Detectors

TL;DR

This paper investigates how weakly entangled states can violate the CHSH inequality more effectively than maximally entangled states in asymmetric Bell experiments with inefficient detectors, revealing scenarios where less entanglement suffices for nonlocality.

Contribution

It derives bounds on entanglement needed for violation at various detection efficiencies and shows violations are possible with arbitrarily low entanglement under certain conditions.

Findings

Violations occur if detection efficiency exceeds 50%.

Weakly entangled states can outperform maximally entangled states in certain scenarios.

CHSH violation can be achieved with any nonzero detection efficiency when inefficiency affects only one measurement.

Abstract

It is well-known that in certain scenarios weakly entangled states can generate stronger nonlocal effects than their maximally entangled counterparts. In this paper, we consider violations of the CHSH Inequality when one party has inefficient detectors, a scenario known as an asymmetric Bell experiment. %We show that violations can occur if and only if the detection efficiency is above $50\%$. For any fixed detection efficiency, we derive a simple upper bound on the entanglement needed to violate the inequality by more than some specified amount $\kappa\geq 0$. When $\kappa=0$, the amount of entanglement in all states violating the inequality goes to zero as the detection efficiency approaches $50\%$ from above. %This provides another scenario in which weakly entangled states are advantageous for violating the CHSH Inequality in the presence of detection inefficiency. We finally consider the scenario in which detection inefficiency arises for only one choice of local measurement. In this case, it is shown that the CHSH Inequality can always be violated for any nonzero detection efficiency and any choice of non-commuting measurements.