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Entropic bounds on coding for noisy quantum channels

Cerf, Nicolas J. (1998) Entropic bounds on coding for noisy quantum channels. Physical Review A, 57 (5). pp. 3330-3347. ISSN 1050-2947. doi:10.1103/PhysRevA.57.3330.

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In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if the loss is zero, quantum information can be perfectly transmitted at a rate measured by the quantum source entropy. By using block coding based on sequences of n entangled symbols, the average loss (defined as the overall loss of the joint n-symbol channel divided by n, when n→∞) can be made lower than the loss for a single use of the channel. In this context, we examine several upper bounds on the rate at which quantum information can be transmitted reliably via a noisy channel, that is, with an asymptotically vanishing average loss while the one-symbol loss of the channel is nonzero. These bounds on the channel capacity rely on the entropic Singleton bound on quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we analyze the Singleton bounds when the noisy quantum channel is supplemented with a classical auxiliary channel.

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Additional Information:©1998 The American Physical Society Received 11 July 1997 We acknowledge C. Adami for numerous useful discussions. This research was supported in part by the National Science Foundation under Grant Nos. PHY 94-12818 and PHY 94-20470, and by a grant from DARPA/ARO through the QUIC Program (No. DAAH04-96-1-3086).
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
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Deposited On:20 Oct 2006
Last Modified:08 Nov 2021 20:26

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