Quantum computation and quantum information
Quantum computation and quantum information
From graph states to two-graph states
Designs, Codes and Cryptography
Geometric entanglement of symmetric states and the majorana representation
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
One and two-variable interlace polynomials: a spectral interpretation
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
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As two of the most important entanglement measures--the entanglement of formation and the entanglement of distillation--have so for been limited to bipartite settings, the study of other entanglement measures for multipartite systems appears necessary. Here, connections between two other entanglement measures--the relative entropy of entanglement and the geometric measure of entanglement--are investigated. It is found that for arbitrary pure states the latter gives rise to a lower bound on the former. For certain pure states, some bipartite and some multipartite, this lower bound is saturated, and thus their relative entropy of entanglement can be found analytically in terms ot their known geometric measure of entanglement. For certain mixed states, upper bounds on the relative entropy of entanglement are also established. Numerical evidence strongly suggests that these upper bounds are tight, i.e., they are actually the relative entropy of entanglement.