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量子ウォークエコー ; Quantum Walk Echo ; リョウシ ウォーク エコー

隆. 遠藤, 祥. 草場, 光 當間, 大地 坂井, 耕一 豊島, 豊. 平良, タカシ エンドウ, ショウ クサバ, ヒカル トウマ, Daichi Sakai, コウイチ トヨシマ, Yutaka Hirayoshi, Endo Takashi, Sho Kusaba, Hikaru Toma, Kouichi Toyoshima, 佐賀大学大学院工学系研究科物理科学専攻, 佐賀大学大学院工学系研究科博士前期課程物理科学専攻

Published Jan 1, 2011• 0 citations
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Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo-like fidelity plays a central role, and when the coin is chaotic this is approximately the characteristic function of a classical random walker. Thus the classical binomial distribution arises as a limit of the quantum walk and the walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement growth is shown to be logarithmic in time as in the case of many-body localization and coupled kicked rotors, and saturates to a value that depends on the relative coin and walker space dimensions. In a coin-dominated scenario, the chaos can thermalize the quantum walk to typical random states such that the entanglement saturates at the Haar averaged Page value, unlike in a walker-dominated case when atypical states seem to be produced.