The Stochastic-Quantum Correspondence

Abstract

This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability. This argument is based on an exact correspondence between the class of `indivisible' stochastic processes and quantum theory. This new stochastic-quantum correspondence demotes the wave function from a primary ontological ingredient to a secondary mathematical tool, and yields a deflationary account of exotic quantum phenomena, such as interference, decoherence, entanglement, noncommutative observables, and wave-function collapse. At a more practical level, the stochastic-quantum correspondence leads to a novel reconstruction of quantum theory, alongside the Hilbert-space, path-integral, and quasiprobability representations, and also provides a framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences.

arXiv comment38 pages, no figures, accepted version for publication, with some material moved into arxiv:2507.21192

References in corpus (7)

• On the reality of the quantum state
• Einstein, incompleteness, and the epistemic view of quantum states
• Fundamentals of Quantum Information Theory
• Dividing Quantum Channels
• Quantum stochastic processes and quantum non-Markovian phenomena
• Quantum advantage in simulating stochastic processes
• Recovering the quantum formalism from physically realist axioms

Cited by in corpus (2)

• The Quantum Measurement Problem: A Review of Recent Trends
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