2002/06/30 by Masahito Hayashi, Masato Koashi, Keiji Matsumoto +2
Computer Science · Physics and Astronomy · #Entropy (arrow of time) #Information theory #Kullback–Leibler divergence #Multipartite entanglement #Probabilistic logic #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #State (computer science) #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1088/0305-4470/36/2/316
published as J. Phys. A: Math. Gen. 36, 527 (2003) · 28 pages, 4 figures, LaTeX2e, iopart.cls, minor corrections
openalex publication_date 2002/12/17 · arxiv created 2002/12/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Consider entanglement concentration schemes that convert n identical copies of a pure state into a maximally entangled state of a desired size with success probability being close to one in the asymptotic limit. We give the distillable entanglement, the number of Bell pairs distilled per copy, as a function of an error exponent , which represents the rate of decrease in failure probability as n tends to infinity. The formula fills the gap between the least upper bound of distillable entanglement in probabilistic concentration, which is the well-known entropy of entanglement, and the maximum attained in deterministic concentration. The method of types in information theory enables the detailed analysis of the distillable entanglement in terms of the error rate. In addition to the probabilistic argument, we consider another type of entanglement concentration scheme, where the initial state is deterministically transformed into a (possibly mixed) final state whose fidelity to a maximally entangled state of a desired size converges to one in the asymptotic limit. We show that the same formula as in the probabilistic argument is valid for the argument on fidelity by replacing the success probability with the fidelity. Furthermore, we also discuss entanglement yield when optimal success probability or optimal fidelity converges to zero in the asymptotic limit (strong converse), and give the explicit formulae for those cases.