Time-continuous open quantum walks (Conference Presentation)
Radhakrishnan Balu, Chaobin Liu · 2017
Continuous-time open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of trace-preserving and completely positive linear maps (or quantum Markov semigroups) on graphs. We show that a CTOQW always converges to a steady state regardless of the initial state when a graph is connected. When the graph is both connected and regular, it is shown that the steady state is the maximally mixed state. The difference of long-time behaviors between CTOQW and other two continuous-time processes on graphs is exemplified. The examples demonstrate that the structure of a graph can affect a quantum coherence effect on CTOQW through a long time run. Precisely, a quantum coherence effect persists throughout the evolution of the CTOQW when the underlying topology is certain irregular graphs (such as a path or a star as shown in the examples). In contrast, a quantum coherence effect will eventually vanish from the open quantum system when the underlying topology is a regular graph (such as a cycle).