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- Deprecated function: SelectQueryExtender::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
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- Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
The coherent information is a quantity used in
quantum
communication theory. It is a property of a
quantum
state and a
quantum
channel Λ; intuitively, it
attempts to describe how much of the
quantum
information in the state will remain after the state goes through
the channel. In this sense, it is analogous to the
classical
mutual information of
classical
information theory. As the classical mutual information gives the
capacity of a
classical
channel, the coherent information gives the
capacity
of a
quantum
channel. The coherent information is written I(A⟩B).
Definition
The coherent information is defined as I(A⟩B) ≡ S(B) − S(AB)
where S(B) is the
Von
Neumann entropy of the output state ρB and S(AB) is the
entropy of the channel
environment
(equivalently, the joint entropy of the output state, and the
purification
ρA) of the
input state. One may think of inputting part of a pure state through the
channel. The part which remains at the input is ρA, and the
channel produces ρB at the
output.
Properties
Uses
The coherent information, when maximised over input states ρA, gives the
quantum
capacity of the
quantum
channel. This is known as the
LSD
Theorem after Lloyd, Shor and Devetak. The quantity is not additive,
and one must go to large block size (i.e. many quantum uses of the
channel).
The coherent information, gives also the
one
way distillable entanglement when maximised over
local
operations performed by
Alice,
and if maximised over
LOCC
operations, it gives the
two-way
distillable entanglement.
History
The coherent information was introduced by
Benjamin
Schumacher and
Michael
A. Nielsen in a 1996 paper Quantum data processing and error
correction, which appeared in Physical Review A.
See Also
References
- Nielsen, Michael A. and Isaac L. Chuang (2000). Quantum
Computation and Quantum Information, Cambridge University Press,
ISBN 0-521-63503-9
- Nielsen, Michael A. and Benjamin Schumacher (1996). Quantum data
processing and error correction. Physical Review A.,
54 (4), 2629-2635.
Category:Quantum
Information Theory
Category:Quantum
Communication
Category:Handbook
of Quantum Information
Last modified:
Monday, October 26, 2015 - 17:56
