Entanglement Transmission and Generation under Channel Uncertainty: Universal Quantum Channel Coding

We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels, so that they are f...

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Bibliographic Details
Published in:	Communications in mathematical physics Vol. 292; no. 1; pp. 55 - 97
Main Authors:	Bjelaković, Igor, Boche, Holger, Nötzel, Janis
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01-11-2009
Subjects:	Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical Direct Part Quantum Code Quantum Channel Achievable Rate Compound Channel
Online Access:	Get full text
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Summary:	We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels, so that they are forced to use quantum codes that are reliable for the whole set of channels. This is precisely the quantum analog of the compound channel coding problem. We determine the entanglement transmission and entanglement-generating capacities of compound quantum channels and show that they are equal. Moreover, we investigate two variants of that basic scenario, namely the cases of informed decoder or informed encoder, and derive corresponding capacity results.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-009-0887-0