Classical quantum stochastic processes

Stochastic Processes and Quantum Mechanics

Quantum Dynamical Entropies for Classical Stochastic Systems

We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit expression for the stochastic dynamical entropy with a clear informationtheoretical interpretation. Finally, we compare our construction with other recent proposals.

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...

Quantum simulations of classical annealing processes.

We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order 1/sqrt delta steps to find an optimal solution with bounded error probability, where delta is the minimum spectral gap of the stocha...

Quantum speedup of classical mixing processes ∗

It is known that repeated measurements performed at uniformly random times enable the continuous-time quantum walk on a finite set S (using a stochastic transition matrix P as the time-independent Hamiltonian) to sample almost uniformly from S provided that P does. Here we show that the same phenomenon holds for other (discrete-time) walk variants and more general measurements types, then focus...