@article{ZNSL_2022_517_a13,
author = {A. Khvedelidze and A. Torosyan},
title = {Comparing classicality of qutrits from {Hilbert{\textendash}Schmidt,} {Bures} and {Bogoliubov{\textendash}Kubo{\textendash}Mori} ensembles},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {250--267},
year = {2022},
volume = {517},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a13/}
}
TY - JOUR AU - A. Khvedelidze AU - A. Torosyan TI - Comparing classicality of qutrits from Hilbert–Schmidt, Bures and Bogoliubov–Kubo–Mori ensembles JO - Zapiski Nauchnykh Seminarov POMI PY - 2022 SP - 250 EP - 267 VL - 517 UR - http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a13/ LA - en ID - ZNSL_2022_517_a13 ER -
A. Khvedelidze; A. Torosyan. Comparing classicality of qutrits from Hilbert–Schmidt, Bures and Bogoliubov–Kubo–Mori ensembles. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 250-267. http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a13/
[1] D. A. Klain and G. C. Rota, Introduction to Geometric Probability, Cambridge University Press, Cambridge, 1997 | MR
[2] E. P. Wigner, “On the quantum correction for thermodynamic equilibrium”, Phys. Rev., 40 (1932), 749–759 | DOI
[3] J. G. Kirkwood, “Quantum statistics of almost classical assemblies”, Phys. Rev., 44 (1933), 31–37 | DOI
[4] P. A. M. Dirac, “On the analogy between classical and quantum mechanics”, Rev. Mod. Phys., 17 (1945), 195–199 | DOI | MR
[5] R. P. Feynman, “Negative probability”, Routledge, 1987, 235–248 | MR
[6] C. Ferrie, R. Morris, and J. Emerson, “Necessity of negativity in quantum theory”, Phys. Rev., A 82 (2010), 044103 | DOI | MR
[7] M. Hillery, “Nonclassical distance in quantum optics”, Phys. Rev., A 35 (1987), 725–732 | DOI
[8] M. Ozawa, “Entanglement measures and the Hilbert–Schmidt distance”, Phys. Lett., A 268 (2000), 158–160 | DOI | MR
[9] V. V. Dodonov, O. V. Man'ko, V. I. Man'ko, and A. Wünsche, “Hilbert–Schmidt distance and non-classicality of states in quantum optics”, J. Mod. Opt., 47:4 (2000), 633–654 | DOI | MR
[10] P. Marian, T. A. Marian, and H. Scutaru, “Quantifying nonclassicality of one-mode Gaussian states of the radiation field”, Phys. Rev. Lett., 88 (2002), 153601 | DOI
[11] A. Kenfack and K. Z̈yczkowski, “Negativity of the Wigner function as an indicator of non-classicality”, J. Opt. B: Quantum and Semiclass. Opt., 6 (2004), 396–404 | DOI | MR
[12] I. I. Arkhipov, A. Barasiński, and J. Svozilík, “Negativity volume of the generalized Wigner function as an entanglement witness for hybrid bipartite states”, Scientific Reports, 8 (2018), 16955 | DOI
[13] V. Abgaryan, A. Khvedelidze, and A. Torosyan, “Kenfack-Z̈yczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit”, Phys. Lett., A 412 (2021), 127591 | DOI | MR
[14] V. Abgaryan, A. Khvedelidze, and A. Torosyan, “The Global indicator of classicality of an arbitrary N-Level quantum system”, J. Math. Sci., 251 (2020), 301–314 | DOI | MR
[15] N. Abbasli, V. Abgaryan, M. Bures, A. Khvedelidze, I. Rogojin, and A. Torosyan, “On measures of classicality/quantumness in quasiprobability representations of finite-dimensional quantum systems”, Phys. Part. Nuclei, 51 (2020), 443–447 | DOI | MR
[16] V. Abgaryan, A. Khvedelidze and I. Rogojin, “On overall measure of non-classicality of N-level quantum system and its universality in the large N limit”, Lecture Notes in Computer Science, 12563, 2021, 244–255 | DOI
[17] E. A. Morozova and N. N. Chentsov, “Markov invariant geometry on manifolds of states”, J. Math. Sci., 56 (1991), 2648–2669 | DOI | MR
[18] D. Petz, “Monotone metrics on matrix spaces”, Linear Algebra and its Applications, 244 (1996), 81–96 | DOI | MR
[19] F. Hiai, H. Kosaki, D. Petz, and M. B. Ruskai, “Families of completely positive maps associated with monotone metrics”, Linear Algebra and its Applications, 439:7 (2013), 1749–1791 | DOI | MR
[20] V. Abgaryan and A. Khvedelidze, “On families of Wigner functions for $N$-level quantum systems”, Symmetry, 13:6 (2021) | DOI
[21] V. Abgaryan, A. Khvedelidze, and A. Torosyan, “On the moduli space of Wigner quasiprobability distributions for N-dimensional quantum systems”, J. Math. Sci., 240 (2019), 617–633 | DOI | MR