The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes

Journal Article · Tue Dec 15 00:00:00 EST 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3271041· OSTI ID:21294514

Hayashi, Masahito ^[1]; Markham, Damian ^[2]; Murao, Mio ^[3]; Owari, Masaki ^[4]; Virmani, Shashank ^[4]

---

1. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579 (Japan)
2. LTCI CNRS, TELECOM ParisTech, 37/39 rue Dareau, 75014 Paris (France)
3. Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan)
4. Optics Section, Blackett Laboratory and Institute for Mathematical Sciences, Imperial College, London SW7 2AZ (United Kingdom)

In this paper for a class of symmetric multiparty pure states, we consider a conjecture related to the geometric measure of entanglement: ''for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a symmetric product state.'' We show that this conjecture is true for symmetric pure states whose amplitudes are all non-negative in a computational basis. The more general conjecture is still open.

• OSTI ID: 21294514
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 12; Other Information: DOI: 10.1063/1.3271041; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GEOMETRY
HILBERT SPACE
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
SYMMETRY