Classical representation of the dynamics of quantum spin chains

TL;DR

This paper introduces a novel classical Markov chain framework to represent quantum spin chain dynamics, resolving issues with negative probabilities and enabling classical modeling of quantum processes.

Contribution

It presents an exact classical Markov chain representation for quantum spin chain dynamics, bridging quantum and classical probabilistic descriptions.

Findings

Classical Markov chains can model quantum spin dynamics.

Negative probabilities are addressed through this classical representation.

Quantum behavior emerges from averaging over classical process realizations.

Abstract

Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of non-commutative observables. In this work, we propose a resolution to this dilemma for quantum spin chains, by introducing an exact representation of their dynamics in terms of classical continuous-time Markov chains (CTMCs). These CTMCs effectively model the creation, annihilation, and propagation of pairs of classical particles and antiparticles. The quantum dynamics then emerges by averaging over various realizations of this classical process.