Law of Large Numbers for Random Quantum Dynamical Semigroups

TL;DR

This paper establishes a Law of Large Numbers for random quantum dynamical semigroups, showing that their averaged iterates converge to a deterministic quantum semigroup, which advances understanding of quantum stochastic processes.

Contribution

It introduces a Law of Large Numbers principle for random quantum dynamical semigroups, linking their averaged behavior to the average generator, a novel theoretical result.

Findings

Random iterates are Chernoff equivalent to the quantum dynamical semigroup.

Convergence of random quantum processes to deterministic limits.

Extension of classical probabilistic laws to quantum stochastic dynamics.

Abstract

We present a Law of Large Numbers principle for uniformly continuous random quantum dynamical semigroups. Random iterates of independent copies of these semigroups are shown to be Chernoff equivalent to the quantum dynamical semigroup by the average generator.