2013/10/31 by Péter Vrana, Peter Vrana, Matthias Christandl · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Bounded function #Field (mathematics) #LOCC #Quantum Computing Algorithms and Architecture #Quantum entanglement #Quantum many-body systems #Transformation (genetics) #quant-ph
paper · pdf · doi:10.1063/1.4908106
published as J. Math. Phys. 56, 022204 (2015) · 11 pages
arxiv created 2014/08/21 · openalex publication_date 2015/02/01 · arxiv updated 2016/05/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.