Coherent information is an
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
measure used in
quantum information theory. It is a property of a
quantum state
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
ρ and 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 ...
; intuitively, it attempts to describe how much of the
quantum information
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...
in the state will remain after the state goes through the channel. In this sense, it is intuitively similar to the
mutual information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such ...
of
classical information theory. The coherent information is written
.
Definition
The coherent information is defined as
where
is the
von Neumann entropy of the output and
is the
entropy exchange between the state and the channel.
History
The coherent information was introduced by
Benjamin Schumacher
Benjamin "Ben" Schumacher is an American theoretical physicist, working mostly in the field of quantum information theory.
He discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a ...
and
Michael A. Nielsen in a 1996 paper ''Quantum data processing and error correction'', which appeared in
Physical Review A
''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost (Max Planck Ins ...
. The same quantity was independently introduced by
Seth Lloyd in a paper called “The capacity of the noisy quantum channel” published in
Physical Review A
''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost (Max Planck Ins ...
.
References
* Nielsen, Michael A. and
Isaac L. Chuang (2000). ''
Quantum Computation and Quantum Information
''Quantum Computation and Quantum Information'' is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang, regarded as a standard text on the subject. It is informally known as "Mike and Ike", after the Mike an ...
'', Cambridge University Press,
*
* {{cite journal , last=Lloyd , first=Seth , author-link=Seth Lloyd, title=Capacity of the noisy quantum channel , journal=Physical Review A , publisher=American Physical Society (APS) , volume=55 , issue=3 , date=1 February 1997 , issn=1050-2947 , doi=10.1103/physreva.55.1613 , pages=1613–1622, arxiv=quant-ph/9604015, bibcode=1997PhRvA..55.1613L , s2cid=5555850
Quantum mechanical entropy
Quantum information theory