Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevA.83.012305
Title: Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
Authors: Chen, L. 
Zhu, H.
Wei, T.-C.
Issue Date: 13-Jan-2011
Citation: Chen, L., Zhu, H., Wei, T.-C. (2011-01-13). Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation. Physical Review A - Atomic, Molecular, and Optical Physics 83 (1) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevA.83.012305
Abstract: We study the geometric measure of entanglement (GM) of pure symmetric states related to rank 1 positive-operator-valued measures (POVMs) and establish a general connection with quantum state estimation theory, especially the maximum likelihood principle. Based on this connection, we provide a method for computing the GM of these states and demonstrate its additivity property under certain conditions. In particular, we prove the additivity of the GM of pure symmetric multiqubit states whose Majorana points under Majorana representation are distributed within a half sphere, including all pure symmetric three-qubit states. We then introduce a family of symmetric states that are generated from mutually unbiased bases and derive an analytical formula for their GM. These states include Dicke states as special cases, which have already been realized in experiments. We also derive the GM of symmetric states generated from symmetric informationally complete POVMs (SIC POVMs) and use it to characterize all inequivalent SIC POVMs in three-dimensional Hilbert space that are covariant with respect to the Heisenberg-Weyl group. Finally, we describe an experimental scheme for creating the symmetric multiqubit states studied in this article and a possible scheme for measuring the permanence of the related Gram matrix. © 2011 American Physical Society.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/112400
ISSN: 10502947
DOI: 10.1103/PhysRevA.83.012305
Appears in Collections:Staff Publications

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