Steady states of continuoustime open quantum walks
Abstract
Continuoustime open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of tracepreserving 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. As shown by the examples in this article, the steady states of CTOQW can be very unusual and complicated even though the underlying graphs are simple. The examples demonstrate that the structure of a graph can affect quantum coherence in CTOQW through a longtime run. Precisely, the quantum coherence 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, the quantum coherence will eventually vanish from the open quantum system when the underlying topology is a regular graph (such as a cycle).
 Publication:

Quantum Information Processing
 Pub Date:
 July 2017
 DOI:
 10.1007/s1112801716258
 arXiv:
 arXiv:1604.05652
 Bibcode:
 2017QuIP...16..173L
 Keywords:

 Semigroups on graphs;
 Continuoustime open quantum walks;
 Steady states;
 Quantum Physics
 EPrint:
 Quantum Inf Process (2017) 16: 173