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arXiv · 2509.19491

Martingale Projections and Quantum Decoherence

Lane P. Hughston·Levent A. Mengütürk
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Abstract

We introduce so-called super/sub-martingale projections as a family of endomorphisms defined on unions of Polish spaces. Such projections allow us to identify martingales as collections of transformations that relate path-valued random variables to each other under conditional expectations. In this sense, super/sub-martingale projections are random functionals that (i) are boundedness preserving and (ii) satisfy a conditional expectation criterion similar to that of the classical martingale theory. As an application to the theory of open quantum systems, we prove (a) that any system-environment interaction that manifests a supermartingale projection on the density matrix gives rise to decoherence, and (b) that any system-environment interaction that manifests a submartingale projection gives rise an increase in Shannon-Wiener information. It follows (c) that martingale projections in an open quantum system give rise both to quantum decoherence and to information gain.

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Lane P. Hughston, Levent A. Mengütürk. 2025-09-23. Martingale Projections and Quantum Decoherence. https://arxiv.org/abs/2509.19491

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