The absolutely maximally entangled (AME) state is a concept in
quantum information science
Quantum information science is a field that combines the principles of quantum mechanics with information theory to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum phys ...
, which has many applications in
quantum error-correcting code, discrete
AdS/CFT correspondence
In theoretical physics, the anti-de Sitter/conformal field theory correspondence (frequently abbreviated as AdS/CFT) is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) that are used ...
,
,
and more. It is the multipartite generalization of the bipartite
maximally entangled state
Quantum entanglement is the phenomenon where the quantum state of each Subatomic particle, particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic o ...
.
Definition
The bipartite maximally entangled state
is the one for which the reduced density operators are maximally mixed, i.e.,
. Typical examples are
Bell states.
A multipartite state
of a system
is called absolutely maximally entangled if for any bipartition
of
, the reduced density operator is maximally mixed
, where
.
Property
The AME state does not always exist; in some given local dimension and number of parties, there is no AME state. There is a list of AME states in low dimensions created by Huber and Wyderka.
The existence of the AME state can be transformed into the existence of the solution for a specific
quantum marginal problem.
The AME can also be used to build a kind of quantum error-correcting code called
holographic error-correcting code.
References
{{reflist
Quantum information science
Quantum states