Probability Representation of Quantum Channels

被引：0
作者：
A. S. Avanesov
V. I. Man’ko
机构：
[1] Moscow Institute of Physics and Technology,Lebedev Physical Institute
[2] Russian Academy of Sciences,Department of Physics
[3] Steklov Mathematical Institute of Russian Academy of Sciences,undefined
[4] Tomsk State University,undefined
来源：
Lobachevskii Journal of Mathematics | 2019年 / 40卷
关键词：
quantum channel; Choi-Jamiolkowski isomorphism; tomographic probability representation of quantum mechanics;
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学科分类号：
摘要：
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct the probability representation of the completely positive maps. In this representation, any completely positive map of qubit state density matrix is identified with the set of classical coin probability distributions. Examples of the maps of qubit states are studied in detail. The evolution equation of quantum states is written in the form of the classical-like kinetic equation for probability distributions identified with qubit state.
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页码：1444 / 1449
页数：5
相关论文
共 72 条
  • [1] Choi M-D(1975)Completely positive linear maps on complex matrices Lin. Algebra Its Appl. 10 285-441
  • [2] Jamioikowski A(1972)Linear transformations which preserve trace and positive semidefiniteness of operators Rep. Math. Phys. 3 275-272
  • [3] Schrödinger E(1926)An undulatory theory of the mechanics of atoms and molecules Phys. Rev. 28 1049-824
  • [4] Landau L(1927)Das Dämpfungsproblem in der Wellenmechanik Z. Phys. 45 430-176
  • [5] von Neumann J(1927)Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik Gött. Nach. 1927 245-924
  • [6] Wigner E(1932)On the quantum correction for thermodynamic equilibrium Phys. Rev. 40 749-775
  • [7] Husimi K(1940)Some formal properties of the density matrix Proc. Phys. Math. Soc. Jpn. 22 264-825
  • [8] Kano Y(1965)A new phase-space distribution function in the statistical theory of the electromagnetic field J. Math. Phys. 6 1913-130
  • [9] Glauber R J(1963)Coherent and incoherent states of the radiation field Phys. Rev. 131 2766-undefined
  • [10] Sudarshan E C G(1963)Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams Phys. Rev. Lett. 10 277-undefined
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