Martingale Projections and Quantum Decoherence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918321421549568 |
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| author | Hughston, Lane P. Mengütürk, Levent A. |
| author_facet | Hughston, Lane P. Mengütürk, Levent A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Martingale Projections and Quantum Decoherence Hughston, Lane P. Mengütürk, Levent A. Quantum Physics Information Theory Probability 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. |
| title | Martingale Projections and Quantum Decoherence |
| topic | Quantum Physics Information Theory Probability |
| url | https://arxiv.org/abs/2509.19491 |