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arXiv:0911.1414 · Physica Scripta

Distances between quantum states in the tomographic-probability representation

Sergey N. Filippov, Vladimir I. Man’ko

Published Sep 1, 2010• 5 citations
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Abstract

Distances between quantum states are reviewed within the framework of the tomographic-probability representation. The tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are distinguished by comparing corresponding probability-distribution functions. Fidelity as well as other distance measures are expressed in terms of tomograms.

DOI
10.1088/0031-8949/2010/t140/014043

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Distances between quantum states are reviewed within the framework of the tomographic-probability representation. The tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are distinguished by comparing corresponding probability-distribution functions. Fidelity as well as other distance measures are expressed in terms of tomograms.
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The relation of theWigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner–Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for directexperimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.
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