Non-Positive Semigroup Dynamics in Continuous Variable Models

TL;DR

This paper demonstrates that using non-positive Markovian semigroups to model subsystem dynamics can lead to physical inconsistencies, especially with entangled initial states, challenging common assumptions in continuous variable models.

Contribution

It reveals limitations of the standard approach to non-positive semigroup dynamics in continuous variable systems with entanglement.

Findings

Eliminating certain initial states causes inconsistencies with entangled subsystems.

Non-positive semigroup models may not be physically valid for all initial conditions.

Entanglement complicates the applicability of traditional Markovian semigroup descriptions.

Abstract

Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the admissible initial conditions those density matrices that would not remain positive by the action of the semigroup dynamics. Using a continuous variable model, we show that this procedure leads to physical inconsistencies when two subsystems are considered and their initial state is entangled.