Violation of Leggett-Garg inequalities in quantum measurements with variable resolution and back-action

TL;DR

This paper investigates how quantum measurements with varying resolution and back-action errors affect the violation of Leggett-Garg inequalities, demonstrating that such violations are consistent across different measurement strengths.

Contribution

It introduces a spin-flip error model to analyze experimental photon polarization data, showing the invariance of Leggett-Garg inequality violations under different measurement conditions.

Findings

Intrinsic joint probability is independent of measurement strength.

Violations of Leggett-Garg inequalities occur regardless of measurement resolution and back-action.

Experimental data confirms theoretical predictions.

Abstract

Quantum mechanics violates Leggett-Garg inequalities because the operator formalism predicts correlations between different spin components that would correspond to negative joint probabilities for the outcomes of joint measurements. However, the uncertainty principle ensures that such joint measurements cannot be implemented without errors. In a sequential measurement of the spin components, the resolution and back-action errors of the intermediate measurement can be described by random spin flips acting on an intrinsic joint probability. If the error rates are known, the intrinsic joint probability can be reconstructed from the noisy statistics of the actual measurement outcomes. In this paper, we use the spin-flip model of measurement errors to analyze experimental data on photon polarization obtained with an interferometric setup that allows us to vary the measurement strength and hence the balance between resolution and back-action errors. We confirm that the intrinsic joint probability obtained from the experimental data is independent of measurement strength and show that the same violation of the Leggett-Garg inequality can be obtained for any combination of measurement resolution and back-action.