Quantum stopping-times

Henry Pierce Stapp

Alexander C. R. Belton, Kalyan B. Sinha

In recent work of the authors, it was shown how to use any finite quantum stop time to stop the CCR flow and its strongly continuous isometric cocycles (Q. J. Math. 65:1145–1164, 2014). The stopped cocycle was shown to satisfy a stopped form of the cocycle identity, valid for deterministic increments of the time used for stopping. Here, a generalization of this identity is obtained, where both cocycle parameters are replaced with finite quantum stop times.

Hao Luo, Xiang Zhan, Peng Zhang +1 more

The stopping time of a one-dimensional bounded classical random walk (RW) is defined as the number of steps taken by a random walker to arrive at a fixed boundary for the first time. A quantum walk (QW) is a non-trivial generalization of RW, and has attracted a great deal of interest from researchers working in quantum physics and quantum information. In this paper, we develop a method to calculate the stopping time for a one-dimensional QW. Using our method, we further compare the properties of stopping time for QW and RW. We find that the mean value of the stopping time is the same for both of these problems. However, for short times, the probability for a walker performing a QW to arrive at the boundary is larger than that for a RW. This means that, although the mean stopping time of a quantum and classical walker are the same, the quantum walker has a greater probability of arriving at the boundary earlier than the classical walker.

Masao Nagasawa

Jung‐Tsung Shen, Michelle L. Povinelli, Sunil Sandhu +1 more

We propose a mechanism to stop and time-reverse single photons in one-dimensional circuit quantum electrodynamics systems. The circuit can be designed to be of deep sub-wavelength scale, and can stop and store two photons in the system at the same time.

Günter Mahler A, Volker A. Weberruß