In the theory of

quantum communication In quantum information theory, a quantum channel is a communication channel that can transmit quantum information, as well as classical information. An example of quantum information is the general dynamics of a qubit. An example of classical in ...

, the entanglement-assisted classical capacity of a

quantum channel In quantum information theory, a quantum channel is a communication channel that can transmit quantum information, as well as classical information. An example of quantum information is the general dynamics of a qubit. An example of classical in ...

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 In quantum information theory, quantum mutual information, or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. It is the quantum mechanical analog of Shannon mutual informat ...

of the channel, which is the input-output

maximized over all pure bipartite

quantum states In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system re ...

with one system transmitted through the

channel Channel, channels, channeling, etc., may refer to: Geography * Channel (geography), a landform consisting of the outline (banks) of the path of a narrow body of water. Australia * Channel Country, region of outback Australia in Queensland and pa ...

. 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 (in theory) to communicate discrete ...

, 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

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 of

quantum entropy In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system. It extends the concept of Gibbs entropy from classical statistical mechanics to quantum statis ...

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

See also

References