Operational Markov Condition for Quantum Processes

Quantum semi-Markov processes.

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow t...

A Coupling Method for Quantum Markov Processes

A necessary condition for weak lumpability in finite Markov processes

Under certain conditions, the state space of a homogeneous Markov process can be partitionned to construct an aggregated markovian process. However, the verification of these conditions requires expensive computations. In this note, we expose a necessary condition for having a markovian aggregated process. This condition is based on properties of the eigenvalues of certain submatrices of the tr...

Accelerated decomposition techniques for large discounted Markov decision processes

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorith...

Classical Markov Processes from Quantum L

We show how classical Markov processes can be obtained from quantum L evy processes. It is shown that quantum L evy processes are quantum Markov processes, and suucient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can rest...