Rajendran Jishnu, Benjamin Colin
School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni 752050, India.
R Soc Open Sci. 2018 Feb 14;5(2):171599. doi: 10.1098/rsos.171599. eCollection 2018 Feb.
Parrondo's paradox is ubiquitous in games, ratchets and random walks. The apparent paradox, devised by J. M. R. Parrondo, that two losing games and can produce a winning outcome has been adapted in many physical and biological systems to explain their working. However, proposals on demonstrating Parrondo's paradox using quantum walks failed for a large number of steps. In this work, we show that instead of a single coin if we consider a two-coin initial state which may or may not be entangled, we can observe a genuine Parrondo's paradox with quantum walks. Furthermore, we focus on reasons for this and pin down the asymmetry in initial two-coin state or asymmetry in shift operator, either of which is necessary for observing a genuine Parrondo's paradox. We extend our work to a three-coin initial state too with similar results. The implications of our work for observing quantum ratchet-like behaviour using quantum walks are also discussed.
帕隆多悖论在博弈、棘轮效应和随机游走中无处不在。由J.M.R.帕隆多提出的这一明显悖论指出，两个输的游戏A和B可以产生一个赢的结果，这已在许多物理和生物系统中得到应用以解释它们的运行机制。然而，关于用量子游走证明帕隆多悖论的提议在大量步数的情况下都失败了。在这项工作中，我们表明，如果我们考虑一个可能纠缠也可能不纠缠的双硬币初始状态，而不是单个硬币，那么我们可以用量子游走观察到真正的帕隆多悖论。此外，我们关注于此的原因并确定初始双硬币状态的不对称性或移位算子的不对称性，这两者中的任何一个对于观察到真正的帕隆多悖论都是必要的。我们还将工作扩展到三硬币初始状态，也得到了类似的结果。我们的工作对于用量子游走观察量子棘轮样行为的意义也进行了讨论。
