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This study resolves a fundamental challenge in quantum probability by providing an exact classical representation of quantum spin chain dynamics using continuous-time Markov chains. By modeling the system as particle-antiparticle pairs whose averaged realizations emerge as quantum behavior, the work offers a rigorous framework to bypass issues with negative probabilities in non-commutative observables. This theoretical advance bridges statistical mechanics and quantum physics, potentially simplifying the simulation and analysis of complex quantum many-body systems.
Classical representation of the dynamics of quantum spin chains
arXiv:2502.10502v3 Announce Type: replace-cross 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.
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.
Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
arXiv:2502.10502 [cond-mat.stat-mech]
(or arXiv:2502.10502v3 [cond-mat.stat-mech] for this version)
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