Gaussian classical capacity of gaussian quantum channels
Abstract
The classical capacity of quantum channels is the tight upper bound for the transmission rate of classical information. This is a quantum counterpart of the foundational notion of the channel capacity introduced by Shannon. Bosonic Gaussian quantum channels provide a good model for optical communications. In order to properly define the classical capacity for these quantum systems, an energy constraint at the channel input is necessary, as in the classical case. A further restriction to Gaussian input ensembles defines the Gaussian (classical) capacity, which can be studied analytically. It also provides a lower bound on the classical capacity and moreover, it is conjectured to coincide with the classical capacity. Therefore, the Gaussian capacity is a useful and important notion in quantum information theory. Recently, we have shown that the study of both the classical and Gaussian capacity of an arbitrary single-mode Gaussian quantum channel can be reduced to the study of a particular fiducial channel. In this work we consider the Gaussian capacity of the fiducial channel, discuss its additivity and analyze its dependence on the channel parameters. In addition, we extend previously obtained results on the optimal channel environment to the single-mode fiducial channel. In particular, we show that the optimal channel environment for the lossy, amplification, and phase-conjugating channels is given by a pure quantum state if its energy is constrained.
Supporting agencies: The authors acknowledge financial support from the F.R.S.-FNRS under the Eranet project HIPERCOM, from the Interuniversity Attraction Poles program of the Belgian Science Policy Office under grant IAP P7-35 “photonics@be”, from the Belgian FRIA foundation, from the Brussels Capital Region under the project CRYPTASC, from the ULB under the program “Ouvertures internationales”, and from the Alexander von Humboldt foundation.
About the Authors
E. Karpov
QuIC, Ecole Polytechnique de Bruxelles, CP 165, Universite Libre de Bruxelles
Belgium
Belgium
1050 Brussels
J. Schafer
QuIC, Ecole Polytechnique de Bruxelles, CP 165, Universite Libre de Bruxelles
Belgium
Belgium
1050 Brussels
O. V. Pilyavets
QuIC, Ecole Polytechnique de Bruxelles, CP 165, Universite Libre de Bruxelles
Belgium
Belgium
1050 Brussels
R. Garcıa-Patron
Max-Planck-Institut fur Quantenoptik; QuIC, Ecole Polytechnique de Bruxelles, CP 165, Universite Libre de Bruxelles
Germany
Germany
Hans-Kopfermann-Straße 1, 85748 Garching
1050 Brussels
N. J. Cerf
QuIC, Ecole Polytechnique de Bruxelles, CP 165, Universite Libre de Bruxelles
Belgium
Belgium
1050 Brussels
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Review
For citations:
Karpov E., Schafer J., Pilyavets O.V., Garcıa-Patron R., Cerf N.J. Gaussian classical capacity of gaussian quantum channels. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(4):496-506.
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