Tomographic portrait of quantum channels. (English) Zbl 1402.81101
Summary: We formulate the notion of quantum channels in the framework of quantum tomography and address there the issue of whether such maps can be regarded as classical stochastic maps. In particular, kernels of maps acting on probability representation of quantum states are derived for qubit and bosonic systems. In the latter case it results that a single mode Gaussian quantum channel corresponds to non-Gaussian classical channels.
MSC:
81P70 | Quantum coding (general) |
81P50 | Quantum state estimation, approximate cloning |
81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
References:
[1] | Manko, O. V.; Man’ko, V. I.; Marmo, G., J. Phys. A: Math. and General, 35, 699, (2002) · Zbl 1041.81080 |
[2] | Mancini, S.; Man’ko, V. I.; Tombesi, P., J. Mod. Optics, 44, 2281, (1997) |
[3] | D’Ariano, G. M.; Maccone, L.; Paris, M. G.A., J. Phys. A: Math. General., 34, 93, (2001) · Zbl 1053.81508 |
[4] | Dodonov, V. V.; Man’ko, V. I., Phys. Lett. A, 229, 335, (1997) · Zbl 1072.81531 |
[5] | Vogel, K.; Risken, H., Phys. Rev. A, 40, 2847, (1989) |
[6] | Mancini, S.; Man’ko, V. I.; Tombesi, P., Quantum and Semiclass. Opt.: J. European Optical Soc. B, 7, 615, (1995) |
[7] | Amosov, G. G.; Korennoi, Y. A.; Man’ko, V. I., Theor. Math. Phys., 171, 832, (2012) · Zbl 1282.81087 |
[8] | Amosov, G. G.; Dnestryan, A. I., Phys. Scr., 90, 074025, (2015) |
[9] | Holevo, A. S., Quantum Systems, Channels, Information, (2012), De Guyter Berlin-Boston · Zbl 1332.81003 |
[10] | Amosov, G. G., Lobachevskii J. Math., 38, 595, (2017) · Zbl 1373.81024 |
[11] | Kraus, K., States, Effects and Operations: Fundamental Notions of Quantum Theory, (1983), Springer Berlin-Heidelberg · Zbl 0545.46049 |
[12] | Filippov, S. N.; Man’ko, V. I., J. Russ. Laser Res., 30, 129, (2009) |
[13] | Ruskai, M. B.; Szarek, S.; Werner, E., Lin. Alg. Appl., 347, 159, (2002) · Zbl 1032.47046 |
[14] | Welsch, D. G.; Vogel, W.; Opatrny, T., Progr. Optics, 39, 63, (1999) |
[15] | Lvovsky, A. I.; Raymer, M. G., Rev. Mod. Phys., 81, 299, (2009) |
[16] | Weedbrook, C., Rev. Mod. Phys., 84, 621, (2012) |
[17] | Hastings, M. B., Nat. Phys., 5, 255, (2009) |
[18] | Shannon, C. E.; Weaver, W., The Mathematical Theory of Communication, (1949), Univ. of Illinois Press Urbana, IL · Zbl 0041.25804 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.