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arXiv:1212.5819 · Physica Scripta

Fidelity and purity of quantum electrical circuit states and quantum tomograms

Olga V. Man’ko

Published Mar 1, 2013• 5 citations
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Abstract

Review of the probability representation of quantum mechanics and the symplectic tomography approach are presented. The examples of Gaussian states of nanoelectric circuit, Josephson junction, and two interacting high-quality resonant circuits are considered. The Shannon entropy, quantum information, fidelity, and purity of quantum states in the tomographic representation of quantum mechanics are studied.

DOI
10.1088/0031-8949/2013/t153/014046

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We review the probabilistic representation of quantum mechanics within which states are described by the probability distribution rather than by the wavefunction and density matrix. Uncertainty relations have been obtained in the form of integral inequalities containing measurable optical tomograms of quantum states. Formulas for the transition probabilities and purity parameter have been derived in terms of the tomographic probability distributions. Inequalities for Shannon and Rényi entropies associated with quantum tomograms have been obtained. A scheme of the star product of tomograms has been developed.
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