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Phase-factor Dependence of the Geometric Entanglement Measure

Kap Soo Jang, MuSeong Kim, DaeKil Park

Journal of the Korean Physical SocietyMay 13, 20110 citations

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

Peiyuan Teng

arXiv:1609.02076Quantum Information ProcessingJun 12, 201712 citations

A geometrical representation of entanglement

Shahabeddin Mostafanazhad aslmarand, Warner A. Miller, Doyeol Ahn +1 more

The European Physical Journal PlusMar 1, 20221 citation

Visualizing elusive phase transitions with geometric entanglement

Román Orús, Tzu-Chieh Wei

We show that by examining the global geometric entanglement it is possible to identify ``elusive'' or hard to detect quantum phase transitions. We analyze several one-dimensional quantum spin chains and demonstrate the existence of nonanalyticities in the geometric entanglement, in particular, across a Kosterlitz-Thouless transition and across a transition for a gapped deformed Affleck-Kennedy-Lieb-Tasaki chain. The observed nonanalyticities can be understood and classified in connection to the nature of the transitions, and are in sharp contrast to the analytic behavior of all the two-body reduced density operators and their derived entanglement measures.We show that by examining the global geometric entanglement it is possible to identify ``elusive'' or hard to detect quantum phase transitions. We analyze several one-dimensional quantum spin chains and demonstrate the existence of nonanalyticities in the geometric entanglement, in particular, across a Kosterlitz-Thouless transition and across a transition for a gapped deformed Affleck-Kennedy-Lieb-Tasaki chain. The observed nonanalyticities can be understood and classified in connection to the nature of the transitions, and are in sharp contrast to the analytic behavior of all the two-body reduced density operators and their derived entanglement measures.

arXiv:0910.2488Physical Review BOct 13, 201070 citations

An observable entanglement measure

Florian Mintert

Bulletin of the American Physical SocietyMar 8, 20070 citations

Robustness of incompatibility for quantum devices

Erkka Haapasalo

A robustness measure for incompatibility of quantum devices in the lines of the robustness of entanglement is proposed. The concept of general robustness measures is first introduced in general convex-geometric settings and these ideas are then applied to measure how incompatible a given pair of quantum devices is. The robustness of quantum incompatibility is calculated in three special cases: a pair of Fourier-coupled rank-1 sharp observables, a pair of decodable channels, where decodability means left-invertibility by a channel, and a pair consisting of a rank-1 sharp observable and a decodable channel.A robustness measure for incompatibility of quantum devices in the lines of the robustness of entanglement is proposed. The concept of general robustness measures is first introduced in general convex-geometric settings and these ideas are then applied to measure how incompatible a given pair of quantum devices is. The robustness of quantum incompatibility is calculated in three special cases: a pair of Fourier-coupled rank-1 sharp observables, a pair of decodable channels, where decodability means left-invertibility by a channel, and a pair consisting of a rank-1 sharp observable and a decodable channel.

arXiv:1502.04881Journal of Physics A Mathematical and TheoreticalJun 5, 201569 citations

A sharp geometric measure of entanglement

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