Entanglement required in achieving entanglement-assisted channel capacities

Details Entanglement required in achieving entanglement-assisted channel capacities Entanglement required in achieving entanglement-assisted channel capacities

2002-05-19

arxiv.org/abs/quant-ph/0205117v1

Phys. Rev. A 66, 052313 (2002)

Physics

Quantum Physics

9 pages, 2 figures, RevTex4

Scientific paper

10.1103/PhysRevA.66.052313

Entanglement shared between the two ends of a quantum communication channel has been shown to be a useful resource in increasing both the quantum and classical capacities for these channels. The entanglement-assisted capacities were derived assuming an unlimited amount of shared entanglement per channel use. In this paper, bounds are derived on the minimum amount of entanglement required per use of a channel, in order to asymptotically achieve the capacity. This is achieved by introducing a class of entanglement-assisted quantum codes. Codes for classes of qubit channels are shown to achieve the quantum entanglement-assisted channel capacity when an amount of shared entanglement per channel given by, E = 1 - Q_E, is provided. It is also shown that for very noisy channels, as the capacities become small, the amount of required entanglement converges for the classical and quantum capacities.

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