Making sense of negative probabilities: An exact representation of the dynamics of quantum spin chains as classical stochastic processes with particle/antiparticle pairs

• URL: http://arxiv.org/abs/2502.10502v1
• Date: Fri, 14 Feb 2025 19:00:11 GMT
• Title: Making sense of negative probabilities: An exact representation of the dynamics of quantum spin chains as classical stochastic processes with particle/antiparticle pairs
• Authors: Tony Jin,
• Abstract summary: A notable issue arises when attempting to define the joint probability of non-commutative observables. We propose an exact representation of the dynamics of quantum spin chains using classical continuous-time Markov chains.
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• 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 by introducing an exact representation of the dynamics of quantum spin chains using 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.

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