Geodesic
Evaluation of non-unital qubit channel capacities
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 258-265 Cet article a éte moissonné depuis la source Math-Net.Ru

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We have applied quantum Sinkhorn's theorem to non-unital qubit channels and derived lower and upper bounds on the classical capacity of such channels.
Keywords: qubit channel, non-unital channel, Holevo capacity. 
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S. N. Filippov. Evaluation of non-unital qubit channel capacities. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 258-265. http://geodesic.mathdoc.fr/item/UZKU_2018_160_2_a5/

[1] Holevo A. S., “The capacity of quantum channel with general signal states”, IEEE Trans. Inf. Theory, 44:1 (1998), 269–273 | DOI | MR | Zbl

[2] Schumacher B., Westmoreland M. D., “Sending classical information via noisy quantum channels”, Phys. Rev. A, 56 (1997), 131–138 | DOI

[3] Holevo A. S., “Quantum coding theorems”, Russ. Math. Surv., 53:6 (1998), 1295–1331 | DOI | MR | Zbl

[4] Holevo A. S., Werner R. F., “Evaluating capacities of bosonic Gaussian channels”, Phys. Rev. A, 63:3 (2001), 032312, 14 pp. | DOI

[5] Holevo A. S., Shirokov M. E. Continuous ensembles and the capacity of infinite-dimensional quantum channels, Theory Probab. Appl., 50:1 (2006), 86–98 | DOI | MR | Zbl

[6] Holevo A. S., Giovannetti V., “Quantum channels and their entropic characteristics”, Rep. Prog. Phys., 75:4 (2012), 046001, 30 pp. | DOI | MR

[7] Holevo A. S., Quantum Systems, Channels, Information, Walter de Gruyter GmbH, Berlin–Boston, 2012, xiii+349 pp. | MR

[8] Aubrun G., Szarek S. J., Alice and Bob meet Banach: The interface of asymptotic geometry analysis and quantum information theory, Mathematical Surveys and Monographs, 223, Am. Math. Soc., 2017, 414 pp. | DOI | MR

[9] Gurvits L., “Classical complexity and quantum entanglement”, J. Comput. Syst. Sci., 69:3 (2004), 448–484 | DOI | MR | Zbl

[10] Filippov S. N., Magadov K. Y., “Positive tensor products of maps and $n$-tensor-stable positive qubit maps”, J. Phys. A: Math. Theor., 50:5 (2017), 55301, 21 pp. | DOI | MR

[11] Filippov S. N., Frizen V. V., Kolobova D. V., “Ultimate entanglement robustness of two-qubit states against general local noises”, Phys. Rev. A, 2018, vol. 97, no. 1, 012322, 9 pp. | DOI | MR

[12] Ruskai M. B., Szarek S., Werner E., “An analysis of completely-positive trace-preserving maps on $m_2$”, Linear Algebra Its Appl., 347:1–3 (2002), 159–187 | DOI | MR | Zbl

[13] King C., “Additivity for unital qubit channels”, J. Math. Phys., 43:10 (2002), 4641–4653 | DOI | MR | Zbl

[14] Wolf M. M., Eisert J., Cubitt T. S., Cirac J. I., “Assessing non-Markovian quantum dynamics”, Phys. Rev. Lett., 101, art. 150402. pp. 1–4 (2008) | DOI | MR

[15] Rivas Á., Huelga S. F., Plenio M. B., “Entanglement and non-Markovianity of quantum evolutions”, Phys. Rev. Lett., 105:5 (2010), 050403, 4 pp. | DOI | MR

[16] Hall M. J. W., Cresser J. D., Li L., Andersson E., “Canonical form of master equations and characterization of non-Markovianity”, Phys. Rev. A, 89:4 (2014), 042120 | DOI

[17] Chruściński D., Wudarski F. A., “Non-Markovianity degree for random unitary evolution”, Phys. Rev. A, 91:1 (2015), 012104, 5 pp. | DOI | MR

[18] Filippov S. N., Piilo J., Maniscalco S., Ziman M., “Divisibility of quantum dynamical maps and collision models”, Phys. Rev. A, 96:3 (2017), 032111, 13 pp. | DOI | MR

[19] Benatti F., Chruściński D., Filippov S., “Tensor power of dynamical maps and positive versus completely positive divisibility”, Phys. Rev. A, 95:1 (2017), 012112, 1–5 pp. | DOI | MR

[20] Moravčíková L., Ziman M., “Entanglement-annihilating and entanglement-breaking channels”, J. Phys. A: Math. Theor., 43:27 (2010), 275306, 11 pp. | DOI | MR | Zbl

[21] Filippov S. N., Rybár T., Ziman M., “Local two-qubit entanglement-annihilating channels”, Phys. Rev. A, 85:1 (2012), 012303, 9 pp. | DOI | MR

[22] Filippov S. N., Ziman M., “Bipartite entanglement-annihilating maps: Necessary and sufficient conditions”, Phys. Rev. A, 88:3 (2013), 032316, 7 pp. | DOI

[23] Filippov S. N., Melnikov A. A., Ziman M., “Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics”, Phys. Rev. A, 88:6 (2013), 062328, 11 pp. | DOI

[24] Filippov S. N. PPT-inducing, distillation-prohibiting, and entanglement-binding quantum channels, J. Russ. Laser Res., 35:5 (2014), 484–491 | DOI

[25] Filippov S. N., Magadov K. Y., Jivulescu M. A., “Absolutely separating quantum maps and channels”, New J. Phys., 19 (2017), 083010, 19 pp. | DOI | MR

[26] Nielsen M. A., Chuang I. L., Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge, 2000, 700 pp. | MR | Zbl