Stochastic evolution of finite level systems: classical vs. quantum

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.

8 pages

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Cited by in corpus (5)

• Probability representation of quantum dynamics using pseudostochastic maps
• Minimal informationally complete measurements for probability representation of quantum dynamics
• On pseudo-stochastic matrices and pseudo-positive maps
• Log-Convex set of Lindblad semigroups acting on $N$-level system
• Discretization of the density matrix as a nonlinear positive map and entanglement