dorsal/arxiv
View SchemaEntanglement-assisted capacity of a quantum channel and the reverse Shannon theorem
| Authors | Charles H. Bennett, Peter W. Shor, John A. Smolin, Ashish V. Thapliyal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106052 |
| URL | https://arxiv.org/abs/quant-ph/0106052 |
Abstract
The entanglement-assisted classical capacity of a noisy quantum channel is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that this capacity is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs $\rho$, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of $\rho$ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement assisted communication--communication over a discrete memoryless channel (DMC) between parties who share prior random information--we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMC's of equal capacity can simulate one another with unit asymptotic efficiency.
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"abstract": "The entanglement-assisted classical capacity of a noisy quantum channel is\nthe amount of information per channel use that can be sent over the channel in\nthe limit of many uses of the channel, assuming that the sender and receiver\nhave access to the resource of shared quantum entanglement, which may be used\nup by the communication protocol. We show that this capacity is given by an\nexpression parallel to that for the capacity of a purely classical channel:\ni.e., the maximum, over channel inputs $\\rho$, of the entropy of the channel\ninput plus the entropy of the channel output minus their joint entropy, the\nlatter being defined as the entropy of an entangled purification of $\\rho$\nafter half of it has passed through the channel. We calculate\nentanglement-assisted capacities for two interesting quantum channels, the\nqubit amplitude damping channel and the bosonic channel with\namplification/attenuation and Gaussian noise. We discuss how many independent\nparameters are required to completely characterize the asymptotic behavior of a\ngeneral quantum channel, alone or in the presence of ancillary resources such\nas prior entanglement. In the classical analog of entanglement assisted\ncommunication--communication over a discrete memoryless channel (DMC) between\nparties who share prior random information--we show that one parameter is\nsufficient, i.e., that in the presence of prior shared random information, all\nDMC\u0027s of equal capacity can simulate one another with unit asymptotic\nefficiency.",
"arxiv_id": "quant-ph/0106052",
"authors": [
"Charles H. Bennett",
"Peter W. Shor",
"John A. Smolin",
"Ashish V. Thapliyal"
],
"categories": [
"quant-ph"
],
"title": "Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem",
"url": "https://arxiv.org/abs/quant-ph/0106052"
},
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