Stochastic evolution of finite level systems: classical vs. quantum

TL;DR

This paper investigates the differences between classical and quantum dynamics of finite-level systems, showing that quantum evolution can violate classical stochasticity, which serves as a signature of quantumness.

Contribution

It introduces a framework where quantum states form a convex subset within a simplex and demonstrates that quantum dynamical maps may not be stochastic, unlike classical maps.

Findings

Quantum states form a convex subset in a probability simplex.

Quantum dynamical maps can violate stochasticity, indicating quantumness.

Classical evolution preserves the entire probability simplex.

Abstract

Quantum dynamics of the density operator in the framework of a single probability vector is analyzed. In this framework quantum states define a proper convex quantum subset in an appropriate simplex. It is showed that the corresponding dynamical map preserving a quantum subset needs not be stochastic contrary to the classical evolution which preserves the entire simplex. Therefore, violation of stochasticity witnesses quantumness of evolution.