In the theory of
quantum communication
Quantum information science is an interdisciplinary field that seeks to understand the analysis, processing, and transmission of information using quantum mechanics principles. It combines the study of Information science with quantum effects in p ...
, the entanglement-assisted classical capacity of a
quantum channel
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information i ...
is the highest rate at which classical information can be transmitted from a sender to receiver when they share an unlimited amount of noiseless
entanglement. It is given by the
quantum mutual information of the channel, which is the input-output
quantum mutual information maximized over all pure bipartite
quantum states with one system transmitted through the
channel. This formula is the natural generalization of Shannon's
noisy channel coding theorem
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (dig ...
, in the sense that this formula is equal to the capacity, and there is no need to regularize it. An additional feature that it shares with Shannon's formula is that a noiseless classical or
quantum feedback channel cannot increase the entanglement-assisted classical capacity. The entanglement-assisted classical capacity theorem is proved in two parts: the direct coding theorem and the converse theorem. The direct coding theorem demonstrates that the
quantum mutual information of the channel is an achievable rate, by a random coding strategy that is effectively a noisy version of the
super-dense coding protocol. The converse theorem demonstrates that this rate is optimal by making use of the
strong subadditivity
Strong may refer to:
Education
* The Strong, an educational institution in Rochester, New York, United States
* Strong Hall (Lawrence, Kansas), an administrative hall of the University of Kansas
* Strong School, New Haven, Connecticut, United S ...
of
quantum entropy.
See also
*
Classical capacity
*
Quantum capacity
*
Typical subspace
In quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems (the most prominent example being Schumacher compression). Its role is analogous to that of the typical set in classical i ...
References
*Christoph Adami and Nicolas J. Cerf. von Neumann capacity of noisy quantum channels. Physical Review A, 56(5):3470-3483, November 1997.
*Charles H. Bennett, Peter W. Shor, John A. Smolin, and Ashish V. Thapliyal. Entanglement-assisted classical capacity of noisy quantum channels. Physical Review Letters, 83(15):3081-3084, October 1999.
*Charles H. Bennett, Peter W. Shor, John A. Smolin, and Ashish V. Thapliyal. Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem. IEEE Transactions on Information Theory, 48:2637-2655, 2002.
*Charles H. Bennett and Stephen J. Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Physical Review Letters, 69(20):2881-2884, November 1992.
*Garry Bowen. Quantum feedback channels. IEEE Transactions on Information Theory, 50(10):2429-2434, October 2004. .
*
{{quantum computing
Quantum information science
Limits of computation