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.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.

arXiv:1206.6954New Journal of PhysicsOct 16, 201297 citations

On the stochastic measurement of incompatible spin components

Franklin E. Schroeck

Foundations of PhysicsMay 1, 198231 citations

Entropic measurement uncertainty relations for all the infinite components of a spin vector

Alberto Barchielli, Matteo Gregoratti

Abstract The information-theoretic formulation of quantum measurement uncertainty relations (MURs), based on the notion of relative entropy between measurement probabilities, is extended to the set of all the spin components for a generic spin s. For an approximate measurement of a spin vector, which gives approximate joint measurements of the spin components, we define the device information loss as the maximum loss of information per observable occurring in approximating the ideal incompatible components with the joint measurement at hand. By optimizing on the measuring device, we define the notion of minimum information loss. By using these notions, we show how to give a significant formulation of state independent MURs in the case of infinitely many target observables. The same construction works as well for finitely many observables, and we study the related MURs for two and three orthogonal spin components. The minimum information loss plays also the role of measure of incompatibility and in this respect it allows us to compare quantitatively the incompatibility of various sets of spin observables, with different number of involved components and different values of s.Abstract The information-theoretic formulation of quantum measurement uncertainty relations (MURs), based on the notion of relative entropy between measurement probabilities, is extended to the set of all the spin components for a generic spin s. For an approximate measurement of a spin vector, which gives approximate joint measurements of the spin components, we define the device information loss as the maximum loss of information per observable occurring in approximating the ideal incompatible components with the joint measurement at hand. By optimizing on the measuring device, we define the notion of minimum information loss. By using these notions, we show how to give a significant formulation of state independent MURs in the case of infinitely many target observables. The same construction works as well for finitely many observables, and we study the related MURs for two and three orthogonal spin components. The minimum information loss plays also the role of measure of incompatibility and in this respect it allows us to compare quantitatively the incompatibility of various sets of spin observables, with different number of involved components and different values of s.

arXiv:1912.09758Journal of Physics CommunicationsApr 30, 20200 citations

Measurement of a spin-1 system

Antonio Di Lorenzo

arXiv:1309.2127Physics Letters AFeb 27, 20153 citations

Entropic measurement uncertainty relations for spin observables

Alberto Barchielli, Matteo Gregoratti

The information-theoretic formulation of quantum measurement uncertainty \nrelations (MURs), based on the notion of relative entropy between measurement \nprobabilities, is extended to the set of all the spin components for a generic \nspin $s$ . For a physical class of approximate joint measurements of the spin \ncomponents, we define the device information loss as the maximum loss of \ninformation per observable occurring in approximating the ideal incompatible \ncomponents with the joint measurement at hand. By optimizing on the measuring \ndevice, we define the notion of minimum information loss. By using this \nnotions, we show how to give a significant formulation of state independent \nMURs in the case of infinitely many target observables. The same construction \nworks as well for finitely many observables, and we study the related MURs for \ntwo and three orthogonal spin components. The minimum information loss plays \nalso the role of measure of incompatibility and in this respect it allows us to \ncompare quantitatively the incompatibility of various sets of spin observables, \nwith different number of involved components and different values of $s$ .The information-theoretic formulation of quantum measurement uncertainty \nrelations (MURs), based on the notion of relative entropy between measurement \nprobabilities, is extended to the set of all the spin components for a generic \nspin $s$. For a physical class of approximate joint measurements of the spin \ncomponents, we define the device information loss as the maximum loss of \ninformation per observable occurring in approximating the ideal incompatible \ncomponents with the joint measurement at hand. By optimizing on the measuring \ndevice, we define the notion of minimum information loss. By using this \nnotions, we show how to give a significant formulation of state independent \nMURs in the case of infinitely many target observables. The same construction \nworks as well for finitely many observables, and we study the related MURs for \ntwo and three orthogonal spin components. The minimum information loss plays \nalso the role of measure of incompatibility and in this respect it allows us to \ncompare quantitatively the incompatibility of various sets of spin observables, \nwith different number of involved components and different values of $s$.

Dec 20, 20190 citations

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. For a physical class of approximate joint measurements of the spin \ncomponents, we define the device information loss as the maximum loss of \ninformation per observable occurring in approximating the ideal incompatible \ncomponents with the joint measurement at hand. By optimizing on the measuring \ndevice, we define the notion of minimum information loss. By using this \nnotions, we show how to give a significant formulation of state independent \nMURs in the case of infinitely many target observables. The same construction \nworks as well for finitely many observables, and we study the related MURs for \ntwo and three orthogonal spin components. The minimum information loss plays \nalso the role of measure of incompatibility and in this respect it allows us to \ncompare quantitatively the incompatibility of various sets of spin observables, \nwith different number of involved components and different values of

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