Brun Todd A, Carteret Hilary A, Ambainis Andris
Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA.
Phys Rev Lett. 2003 Sep 26;91(13):130602. doi: 10.1103/PhysRevLett.91.130602. Epub 2003 Sep 25.
We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior and find analytical expressions for this in the long-time limit; we see that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth of the variance even for weak decoherence.
驱动游走的量子“硬币”中的退相干，或者使用高维（或多个）硬币来削弱干涉效应。我们将位置方差用作经典行为的指标，并在长时间极限下找到其解析表达式；我们发现，多硬币游走除了在每一步都有一个新硬币的极限情况下，保留了方差的“量子”二次增长，而有退相干的游走即使在弱退相干情况下也呈现方差的“经典”线性增长。
