In the theory of
quantum communication, the entanglement-assisted classical capacity of a
quantum channel 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
Channel, channels, channeling, etc., may refer to:
Geography
* Channel (geography), in physical geography, a landform consisting of the outline (banks) of the path of a narrow body of water.
Australia
* Channel Country, region of outback Austral ...
. 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 (di ...
, 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 Quantum feedback or quantum feedback control is a class of methods to prepare and manipulate a quantum system in which that system's quantum state or trajectory is used to evolve the system towards some desired outcome. Just as in the classical case ...
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
In quantum information theory, superdense coding (also referred to as ''dense coding'') is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assum ...
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
In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density matrix ...
.
See also
*
Classical capacity
*
Quantum capacity
In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel from a sender to a receiver. It is also equal to the highest ra ...
*
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