Wigner Measures and Coherent Quantum Control
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 59-66.

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We introduce Wigner measures for infinite-dimensional open quantum systems; important examples of such systems are encountered in quantum control theory. In addition, we propose an axiomatic definition of coherent quantum feedback.
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J. E. Gough; T. S. Ratiu; O. G. Smolyanov. Wigner Measures and Coherent Quantum Control. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 59-66. http://geodesic.mathdoc.fr/item/TM_2021_313_a5/

[1] Bondar D.I., Pechen A.N., “Uncomputability and complexity of quantum control”, Sci. Rep., 10 (2020), 1195 | DOI

[2] Gough J., James M.R., “Quantum feedback networks: Hamiltonian formulation”, Commun. Math. Phys., 287:3 (2009), 1109–1132 | DOI | MR | Zbl

[3] J. Gough, T. S. Ratiu, and O. G. Smolyanov, “Feynman, Wigner, and Hamiltonian structures describing the dynamics of open quantum systems”, Dokl. Math., 89:1 (2014), 68–71 | DOI | MR | Zbl

[4] J. Gough, T. S. Ratiu, and O. G. Smolyanov, “Wigner measures and quantum control”, Dokl. Math., 91:2 (2015), 199–203 | DOI | MR | Zbl

[5] V. V. Kozlov and O. G. Smolyanov, “Wigner function and diffusion in a collision-free medium of quantum particles”, Theory Probab. Appl., 51:1 (2007), 168–181 | DOI | MR | Zbl

[6] V. V. Kozlov and O. G. Smolyanov, “Wigner measures on infinite-dimensional spaces and the Bogolyubov equations for quantum systems”, Dokl. Math., 84:1 (2011), 571–575 | DOI | MR | Zbl

[7] Lloyd S., “Coherent quantum feedback”, Phys. Rev. A, 62:2 (2000), 022108 | DOI | MR

[8] Loève M., Probability theory, v. 1, Grad. Texts Math., 45, Springer, New York, 1977 | MR | Zbl

[9] Mazzucchi S., Mathematical Feynman path integrals and their applications, World Scientific, Hackensack, NJ, 2009 | MR | Zbl

[10] Montaldi J., Smolyanov O.G., “Transformations of measures via their generalized densities”, Russ. J. Math. Phys., 21:3 (2014), 379–385 | DOI | MR | Zbl

[11] Principles and applications of quantum control engineering: Papers of a Theo Murphy Meeting Issue (Kavli R. Soc. Int. Cent., Chicheley Hall, 2011), Philos. Trans. R. Soc. London. Ser. A: Math. Phys. Eng. Sci., 370, no. 1979, ed. by J. E. Gough et al., R. Soc. Publ., London, 2012 | MR

[12] T. S. Ratiu and O. G. Smolyanov, “Hamiltonian and Feynman aspects of secondary quantization”, Dokl. Math., 87:3 (2013), 289–292 | DOI | MR | Zbl

[13] O. G. Smolyanov, “Measurable polylinear and power functionals in certain linear spaces with a measure”, Sov. Math., Dokl., 7 (1966), 1242–1246 | MR | Zbl

[14] Smolyanov O.G., Shavgulidze E.T., Kontinualnye integraly, URSS, M., 2015

[15] Smolyanov O.G., Tokarev A.G., Truman A., “Hamiltonian Feynman path integrals via the Chernoff formula”, J. Math. Phys., 43:10 (2002), 5161–5171 | DOI | MR | Zbl