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On the gain of entanglement assistance in the classical capacity of quantum Gaussian channels. (English. Russian original) Zbl 1323.81014
Math. Notes 97, No. 6, 974-977 (2015); translation from Mat. Zametki 97, No. 6, 951-954 (2015).
From the text: The main characteristics determining the information properties of a quantum channel include its classical entanglement-assisted and unassisted capacities. The classical (unassisted) capacity $$C(\Phi)$$ of a channel $$\Phi$$ determines the limit rate of classical information transmission through $$\Phi$$ with any block coding at the input and the corresponding measurement at the output, and the classical entanglement-assisted channel capacity $$C_{ea}(\Phi)$$ supposes, in addition, the presence of an entangled state between the input and the output of the channel $$\Phi$$ (a detailed description of transmission protocols can be found in Chapter 8 of [the first author, Quantum systems, channels, information. A mathematical introduction. Berlin: de Gruyter (2012; Zbl 1332.81003)]). Since entanglement is an additional resource, it follows that $$C_{ea}(\Phi) \geq C(\Phi)$$ for any channel $$\Phi$$.
##### MSC:
 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 94A40 Channel models (including quantum) in information and communication theory 81P70 Quantum coding (general) 81P40 Quantum coherence, entanglement, quantum correlations 94A17 Measures of information, entropy 94A24 Coding theorems (Shannon theory)
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##### References:
 [1] A. S. Holevo, Quantum Systems, Channels, Information (MTsNMO, Moscow, 2010) [in Russian]. [2] Bennett, CH; Shor, PW; Smolin, J A; Thapliyal, AV, No article title, IEEE Trans. Inform. Theory, 48, 2637, (2002) · Zbl 1062.94011 [3] Holevo, A S, No article title, Teor. Veroyatnost. Primenen., 48, 359, (2003) [4] Holevo, A S; Shirokov, M E, No article title, Problemy Peredachi Informatsii, 49, 19, (2013) [5] Shirokov, M E, No article title, Problemy Peredachi Informatsii, 48, 3, (2012) [6] Giovannetti, V; Holevo, A S; Garcá-Patrón, R, No article title, Commun. Math. Phys., 334, 1553, (2015) · Zbl 1308.81046 [7] Holevo, A S, No article title, Uspekhi Mat. Nauk, 70, 141, (2015) [8] A. S. Holevo, On the Constrained Classical Capacity of Infinite-Dimensional Covariant Channels, arXiv: 1409.8085. · Zbl 1330.81055 [9] Holevo, A S, No article title, Problemy Peredachi Informatsii, 50, 3, (2014)
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