Truncated Wigner approximation as a non-positive Kraus map

Abstract

We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator $\hat{R}(t)$, which does not describe a physical state. The rate of appearance of negative eigenvalues of $\hat{R}(t)$ can be efficiently estimated. The short-time dynamics of the Kerr and second harmonic generation Hamiltonains are discussed.

References in corpus (1)

• Wigner flow reveals topological order in quantum phase space dynamics

Cited by in corpus (2)

• Learning Potentials of Quantum Systems using Deep Neural Networks
• Distinguishing quantum features in classical propagation