Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem

By Charles H. Bennett, Peter W. Shor, John A. Smolin, Ashish V. Thapliyal. IEEE Transactions on Information Theory, 2001

705 citations recorded by the source corpus.

The entanglement-assisted classical capacity of a noisy quantum channel (C/sub E/) 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 the capacity C/sub E/ is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs /spl 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 /spl 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 DMCs of equal capacity can simulate one another with unit asymptotic efficiency.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ed059570b3c107768b863e5b2ca473e912f061de

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Citations in the corpus

Completely positive maps and classical correlations (2007, methodology): “Suggestions for characterizing the correlations along similar lines were also made by Bennett et al in [23, 24].”
The Communication Complexity of Correlation (2007, neutral): “Our first result shows that there is such a characterization if ALICE and BOB are allowed to share random information, generated independently of ALICE’s input (shared randomness has recently been found useful in a similar information theoretic setting [9]).”
Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future (2019, background): “This is due to the reason that quantum channels can have different possibilities in terms of delivering information including quantum information, entanglement-assisted classical information [123] and private classical information [124].”
Quantum, classical, and total amount of correlations in a quantum state (2004, background): “While this deﬁnition is formally very simple, an operational interpretation for it was hitherto missing [6] (at least not for the quantity itself with given state; it plays however a crucial role in the formula for the entanglement-assisted capacity of a quantum channel [7]).”
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory (2009, methodology): “Motivated by this, they conjectured the Quantum Reverse Shannon Theorem (QRST) in [2].”
The mother of all protocols: restructuring quantum information’s family tree (2006, methodology): “…other discoveries, the determination of the classical capacity of a quantum channel [1, 2], the capacities of entanglement-assisted channels [3, 4], the quantum capacity of a quantum channel [5, 6, 7], and the best ways to use noisy entanglement to extract pure entanglement [8] or to help send…”
Quantum channels and memory effects (2012, background): “This also leads to revise the Hamming bound (108) with 2n+m on the r.h.s. (Bennett et al., 2002).”
The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information (2003, background): “The original paper on the entanglement assisted capacity [4] describes how to achieve”
On quantum statistical inference (2003, methodology): “This scheme was invented by Bennett et al. (1993) and experimentally carried out by A. Zeilinger’s group in Innsbruck, see Bouwmeester et al. (1997). For a recent survey including references to the results of other experimental groups see Bouwmeester et al. (2001). The method illustrates how quantum”
Categories and Subject Descriptors (2001, neutral): “As noted above, the problem of simulating the sending of the output of a channel with feedback has been studied in the literature under the name of classical reverse Shannon theorem [9, 25, 8].”