TY - JOUR
T1 - Multipartite mixed maximally entangled states
T2 - mixed states with entanglement 1
AU - Hedemann, Samuel R.
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/4
Y1 - 2022/4
N2 - We present a full definition of mixed maximally entangled (MME) states for multipartite systems, generalizing their existing definition for bipartite systems by using multipartite Schmidt decomposition and deriving a set of necessary and sufficient conditions for their existence. Additionally, we give worked examples and provide a large collection of tabulated multipartite MME states in a variety of systems. MME states are a special kind of maximally entangled mixed state (MEMS) for which every pure decomposition state in all decompositions is maximally entangled. Thus, MME states have entanglement 1 by all valid unit-normalized entanglement measures, whereas general MEMS can have entanglement less than 1. Multipartite MME states likely have important applications such as remote state preparation and also set critical performance goals for entanglement measures.
AB - We present a full definition of mixed maximally entangled (MME) states for multipartite systems, generalizing their existing definition for bipartite systems by using multipartite Schmidt decomposition and deriving a set of necessary and sufficient conditions for their existence. Additionally, we give worked examples and provide a large collection of tabulated multipartite MME states in a variety of systems. MME states are a special kind of maximally entangled mixed state (MEMS) for which every pure decomposition state in all decompositions is maximally entangled. Thus, MME states have entanglement 1 by all valid unit-normalized entanglement measures, whereas general MEMS can have entanglement less than 1. Multipartite MME states likely have important applications such as remote state preparation and also set critical performance goals for entanglement measures.
KW - MME
KW - Mixed maximal entanglement
KW - Multipartite
KW - Multipartite Schmidt decomposition
KW - TGX states
KW - True-generalized X states
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U2 - 10.1007/s11128-022-03458-0
DO - 10.1007/s11128-022-03458-0
M3 - Article
AN - SCOPUS:85127405427
SN - 1570-0755
VL - 21
JO - Quantum Information Processing
JF - Quantum Information Processing
IS - 4
M1 - 133
ER -