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This article is cited in 26 scientific papers (total in 26 papers)
Entanglement-assisted capacities of constrained quantum channels
A. S. Holevo
Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
In this paper we fill a gap in previous works by proving the conjectured formula for the classical entanglement-assisted capacity of a quantum channel with additive constraint (such as the Bosonic Gaussian channel). Our main tools are the coding theorem for classical-quantum constrained channels and a finite-dimensional approximation of the input density operators for entanglement-assisted capacity. We also give sufficient conditions under which suprema in the capacity formulas are achieved.
Keywords:
quantum communication channel, classical capacity, entangled state.
DOI:
https://doi.org/10.4213/tvp289
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English version:
Theory of Probability and its Applications, 2004, 48:2, 243–255
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Received: 26.11.2002
Citation:
A. S. Holevo, “Entanglement-assisted capacities of constrained quantum channels”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 359–374; Theory Probab. Appl., 48:2 (2004), 243–255
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/tvp289https://doi.org/10.4213/tvp289 http://mi.mathnet.ru/eng/tvp/v48/i2/p359
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This publication is cited in the following articles:
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A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98
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M. E. Shirokov, “Entropy characteristics of subsets of states. I”, Izv. Math., 70:6 (2006), 1265–1292
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A. S. Holevo, “Multiplicativity of $p$-norms of completely positive maps and the additivity problem in quantum information theory”, Russian Math. Surveys, 61:2 (2006), 301–339
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M. E. Shirokov, “On properties of quantum channels related to their classical capacity”, Theory Probab. Appl., 52:2 (2008), 250–276
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Ganikhodjaev N., Mukhamedov F., “On entropy transmission for quantum channels”, Appl. Math. Inf. Sci., 1:3 (2007), 275–286
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M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90
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A. S. Holevo, “Entanglement-Breaking Channels in Infinite Dimensions”, Problems Inform. Transmission, 44:3 (2008), 171–184
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M. E. Shirokov, “On Channels with Finite Holevo Capacity”, Theory Probab. Appl., 53:4 (2009), 648–662
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A. S. Holevo, “Information capacity of a quantum observable”, Problems Inform. Transmission, 48:1 (2012), 1–10
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M. E. Shirokov, “Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel”, Problems Inform. Transmission, 48:2 (2012), 85–101
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A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31
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A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels”, Theory Probab. Appl., 58:2 (2014), 264–285
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A. A. Kuznetsova, A. S. Holevo, “Coding theorems for hybrid channels. II”, Theory Probab. Appl., 59:1 (2015), 145–154
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Caruso F. Giovannetti V. Lupo C. Mancini S., “Quantum Channels and Memory Effects”, Rev. Mod. Phys., 86:4 (2014), 1203–1259
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A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russian Math. Surveys, 70:2 (2015), 331–367
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A. S. Holevo, M. E. Shirokov, “On the Gain of Entanglement Assistance in the Classical Capacity of Quantum Gaussian Channels”, Math. Notes, 97:6 (2015), 974–977
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A. S. Holevo, M. E. Shirokov, “Criterion of weak compactness for families of generalized quantum ensembles and its applications”, Theory Probab. Appl., 60:2 (2016), 320–325
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M. E. Shirokov, “Measures of correlations in infinite-dimensional quantum systems”, Sb. Math., 207:5 (2016), 724–768
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Winter A., “Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints”, Commun. Math. Phys., 347:1 (2016), 291–313
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M. E. Shirokov, A. S. Holevo, “On lower semicontinuity of the entropic disturbance and its applications in quantum information theory”, Izv. Math., 81:5 (2017), 1044–1060
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Sharma K., Wilde M.M., Adhikari S., Takeoka M., “Bounding the Energy-Constrained Quantum and Private Capacities of Phase-Insensitive Bosonic Gaussian Channels”, New J. Phys., 20 (2018), 063025
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Davis N. Shirokov M.E. Wilde M.M., “Energy-Constrained Two-Way Assisted Private and Quantum Capacities of Quantum Channels”, Phys. Rev. A, 97:6 (2018), 062310
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M. E. Shirokov, “On the energy-constrained diamond norm and its application in quantum information theory”, Problems Inform. Transmission, 54:1 (2018), 20–33
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Wilde M.M. Qi H., “Energy-Constrained Private and Quantum Capacities of Quantum Channels”, IEEE Trans. Inf. Theory, 64:12 (2018), 7802–7827
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Ding D., Pavlichin D.S., Wilde M.M., “Quantum Channel Capacities Per Unit Cost”, IEEE Trans. Inf. Theory, 65:1 (2019), 418–435
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Oskouei S.Kh., Mancini S., Wilde M.M., “Union Bound For Quantum Information Processing”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 475:2221 (2019), 20180612
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