2012/05/20 by Wataru Kumagai, Masahito Hayashi, Kumagai, Wataru +1
Computer Science · Materials Science · Physics and Astronomy · #Machine Learning in Materials Science #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #quant-ph
paper · pdf · doi:10.48550/arxiv.1205.4370
6 pages, 1 figure
arxiv created 2012/05/20 · arxiv updated 2012/05/22
For a pure state ψ on a composite system HA\otimesHB, both the entanglement cost EC(ψ) and the distillable entanglement ED(ψ) coincide with the von Neumann entropy H(TrBψ). Therefore, the entanglement concentration from the multiple state ψ⊗ n of a pure state ψ to the multiple state Φ⊗ Ln of the EPR state Φ seems to be able to be reversibly performed with an asymptotically infinitesimal error when the rate Ln/n goes to H(TrBψ). In this paper, we show that it is impossible to reversibly perform the entanglement concentration for a multiple pure state even in asymptotic situation. In addition, in the case when we recover the multiple state ψ⊗ Mn after the concentration for ψ⊗ n, we evaluate the asymptotic behavior of the loss number n-Mn of ψ. This evaluation is thought to be closely related to the entanglement compression in distant parties.