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Experimental investigation of the role of measurement uncertainties in the violation of Leggett-Garg inequalities

Yutaro Suzuki, M. Iinuma, Tomonori Okazaki, Gen Taguchi, Yutaka Kadoya, Holger Friedrich Hofmann

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We show that the violation of Leggett-Garg inequalities can be confirmed by intermediate measurements of arbitrary strength if both measurement resolution and back-action uncertainties are taken into account.
DOI
10.1364/iqec.2011.i394

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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.