期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 50, 期 4, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aa5191
关键词
first passage time; quantum walk; renewal equation
资金
- Israel Science Foundation [376/12]
We investigate the statistics of the first detected passage time of a quantum walk. The postulates of quantum theory, in particular the collapse of the wave function upon measurement, reveal an intimate connection between the wave function of a process free of measurements, i.e. the solution of the Schrodinger equation, and the statistics of first detection events on a site. For stroboscopic measurements a quantum renewal equation yields basic properties of quantum walks. For example, for a tight binding model on a ring we discover critical sampling times, diverging quantities such as the mean time for first detection, and an optimal detection rate. For a quantum walk on an infinite line the probability of first detection decays like (time)(-3) with a superimposed oscillation, critical behavior for a specific choice of sampling time, and vanishing amplitude when the sampling time approaches zero due to the quantum Zeno effect.
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