Objective trajectories in hybrid classical-quantum dynamics

TL;DR

This paper introduces stochastic, linear, and completely positive hybrid classical-quantum dynamics models, providing new toy models and unravelling methods to study their trajectories without relying on the quantum measurement postulate.

Contribution

It presents novel toy models and an unravelling approach for hybrid classical-quantum evolution, avoiding quantum measurement postulates and enabling trajectory uniqueness.

Findings

Trajectories can be unique conditioned on classical degrees of freedom.

The models avoid pathologies of semi-classical equations.

Numerical simulation code is provided.

Abstract

Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the back-reaction of quantum fields on space-time which does not suffer from the pathologies of the semi-classical equations. Here we introduce several toy models in which to study hybrid classical-quantum evolution, including a qubit coupled to a particle in a potential, and a quantum harmonic oscillator coupled to a classical one. We present an unravelling approach to calculate the dynamics, and provide code to numerically simulate it. Unlike the purely quantum case, the trajectories (or histories) of this unravelling can be unique, conditioned on the classical degrees of freedom for discrete realisations of the dynamics, when different jumps in the classical degrees of freedom are accompanied by the action of unique operators on the quantum system. As a result, the ``measurement postulate'' of quantum theory is not needed; quantum systems become classical because they interact with a fundamentally classical field.