Asymptotic entanglement transformation between W and GHZ states

Vrana, Péter and Christandl, Matthias (2015) Asymptotic entanglement transformation between W and GHZ states. JOURNAL OF MATHEMATICAL PHYSICS, 56. ISSN 0022-2488

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Abstract

We investigate entanglement transformations with stochastic local operations and classical com- munication (SLOCC) 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 increase 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.

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