Quantum walks in the density operator picture

摘要: A new approach to quantum walks is presented. Considering a system undergoing some unitary discrete-time evolution in directed graph G, we think of the vertices G as sites that are occupied by system, whose internal state described density operators. To formulate evolution, define reflections tensor product an Hilbert space and spatial space. We then construct channels govern graph. The discrete dynamics (called walks) obtained iterating channel on operator system. It turns out this framework, action usual matrix multiplication.