Physics – Quantum Physics
Scientific paper
2007-12-06
Open Syst. Inf. Dyn. 15 (2008) 71-89
Physics
Quantum Physics
9 pages, two-column style. This paper is a companion to quant-ph/0702005 and quant-ph/0702006
Scientific paper
10.1142/S1230161208000079
Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum channel. The codes are random subspaces selected according to the Haar measure, but distorted as a function of the sender's input density operator. Using large deviations techniques, we show that classical data transmitted in either of two Fourier-conjugate bases for the coding subspace can be decoded with low probability of error. A recently discovered information-uncertainty relation then implies that the quantum mutual information for entanglement encoded into the subspace and transmitted through the channel will be high. The monogamy of quantum correlations finally implies that the environment of the channel cannot be significantly coupled to the entanglement, and concluding, which ensures the existence of a decoding by the receiver.
Hayden Patrick
Shor Peter W.
Winter Andreas
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