TY - JOUR
T1 - Ent
T2 - A multipartite entanglement measure, and parameterization of entangled states
AU - Hedemann, Samuel R.
N1 - Publisher Copyright:
© Rinton Press.
PY - 2018/5
Y1 - 2018/5
N2 - A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally entangled states in every multipartite system such that they are true-generalized X states (TGX) states, a generalization of the Bell states, and are extended to general nonTGX states as well. These results are then used to prove the existence of maximally entangled basis (MEB) sets in all systems. A parameterization of general pure states of all ent values is given, and proposed as a multipartite Schmidt decomposition. Finally, we develop an ent vector and ent array to handle more general definitions of multipartite entanglement, and the ent is extended to general mixed states, providing a general multipartite entanglement measure.
AB - A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally entangled states in every multipartite system such that they are true-generalized X states (TGX) states, a generalization of the Bell states, and are extended to general nonTGX states as well. These results are then used to prove the existence of maximally entangled basis (MEB) sets in all systems. A parameterization of general pure states of all ent values is given, and proposed as a multipartite Schmidt decomposition. Finally, we develop an ent vector and ent array to handle more general definitions of multipartite entanglement, and the ent is extended to general mixed states, providing a general multipartite entanglement measure.
KW - 13-Step algorithm
KW - Ent
KW - Entanglement measure
KW - Multipartite entanglement
KW - Quantum entanglement
KW - Schmidt decomposition
KW - TGX states
KW - Theta states
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U2 - 10.26421/qic18.5-6-2
DO - 10.26421/qic18.5-6-2
M3 - Article
AN - SCOPUS:85045398351
SN - 1533-7146
VL - 18
SP - 389
EP - 442
JO - Quantum Information and Computation
JF - Quantum Information and Computation
IS - 5-6
ER -