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Probability Representation of Quantum Observables and Quantum States

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Journal of Russian Laser Research Aims and scope

Abstract

We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation for quantum observables (Heisenberg equation) in the probability representation and give examples of the spin-1/2 (qubit) states and the spin observables. We present quantum channels for qubits in the probability representation.

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Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

    Vladimir N. Chernega, Olga V. Man’ko & Vladimir I. Man’ko

  2. Bauman Moscow State Technical University, The 2nd Baumanskaya Str. 5, Moscow, 105005, Russia

    Olga V. Man’ko

  3. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow Region, 141700, Russia

    Vladimir I. Man’ko

Authors
  1. Vladimir N. Chernega
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  2. Olga V. Man’ko
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  3. Vladimir I. Man’ko
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Correspondence to Olga V. Man’ko.

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Chernega, V.N., Man’ko, O.V. & Man’ko, V.I. Probability Representation of Quantum Observables and Quantum States. J Russ Laser Res 38, 324–333 (2017). https://doi.org/10.1007/s10946-017-9648-2

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  • DOI: https://doi.org/10.1007/s10946-017-9648-2

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