Quantum stochastic walks.
(a) Venn diagram showing the relationship between quantum walks (QWs–unitary evolution defined by the von Neumann equation) and classical random walks (CRWs–irreversible dynamics in a master equation) as two limiting cases within the family of quantum stochastic walks (QSWs) which includes more general probability distributions. We make use of the subset of QSWs interpolating between both cases through the parameter α ∈ [0, 1]. (b) Axiomatic construction of QSWs from an underlying graph. Each element of the connectivity matrix of the network corresponds to an allowed transition in the dynamical process. CRWs are defined from Axioms 1-2, QWs from Axioms 3-5 and Axiom 6 is only associated to those QSWs with no counterpart as just CRWs or QWs for their formalization. See Whitfield et al.36 for further reading.