Asymptotic entanglement transformation between W and GHZ states

Journal Article · Sun Feb 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4908106· OSTI ID:22403103

Vrana, Péter ^[1]; Christandl, Matthias ^[1]

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1. Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich (Switzerland)

We investigate entanglement transformations with stochastic local operations and classical communication in an asymptotic setting using the concepts of degeneration and border rank of tensors from algebraic complexity theory. Results well-known in that field imply that GHZ states can be transformed into W states at rate 1 for any number of parties. As a generalization, we find that the asymptotic conversion rate from GHZ states to Dicke states is bounded as the number of subsystems increases and the number of excitations is fixed. By generalizing constructions of Coppersmith and Winograd and by using monotones introduced by Strassen, we also compute the conversion rate from W to GHZ states.

• OSTI ID: 22403103
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 2; Other Information: (c) 2015 AIP Publishing LLC; 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
ASYMPTOTIC SOLUTIONS
CONVERSION
EXCITATION
QUANTUM ENTANGLEMENT
STOCHASTIC PROCESSES
TENSORS
TRANSFORMATIONS