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Asymptotic entanglement transformation between W and GHZ states

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arxiv 1310.3244 v2 pith:XQUNITYJ submitted 2013-10-11 quant-ph

Peter Vrana , Matthias Christandl This is my paper · ORCID
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keywords statesasymptoticnumberrateconversionentanglementalgebraicborder
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We investigate entanglement transformations with stochastic local operations and classical communication (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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  1. Asymptotic tensor rank is characterized by polynomials

    cs.CC 2024-11 conditional novelty 8.0 of 10

    Sublevel sets of asymptotic tensor rank are Zariski-closed, making the parameter well-ordered in value, complete over the complex numbers, and computable from above.

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