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

Abstract

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