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Title: Asymptotic entanglement transformation between W and GHZ states

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.
Authors:
 [1] ;  [2] ;  [1] ;  [3]
  1. Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich (Switzerland)
  2. (Hungary)
  3. (Denmark)
Publication Date:
OSTI Identifier:
22403103
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; CONVERSION; EXCITATION; QUANTUM ENTANGLEMENT; STOCHASTIC PROCESSES; TENSORS; TRANSFORMATIONS