A no-go theorem for irreversibility in arbitrary realizations of the collapse dynamics

A. Della Corte; L. Guglielmi; M. Farotti

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arXiv · 2512.12862

A no-go theorem for irreversibility in arbitrary realizations of the collapse dynamics

A. Della Corte·L. Guglielmi·M. Farotti

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Abstract

We study finite dimensional quantum systems with arbitrary collapse events, establishing a structural no-go for operational irreversibility along arbitrary realizations of the collapse dynamics. More precisely, we prove that, for every choice of a physically admissible trajectory (i.e., collapse outcomes having nonzero Born weight) assigned to each state, there exists a nonempty topologically closed subset of the projective state space within which any two states can be connected with arbitrarily fine Fubini-Study precision and arbitrarily small integrated energetic cost. This shows that the preservation of information along observed realizations of outcomes guarantees islands of quasi-reversibility, while genuine irreversibility requires additional ingredients such as non-compactness or information erasure.

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A. Della Corte, L. Guglielmi, M. Farotti. 2026-09-21. A no-go theorem for irreversibility in arbitrary realizations of the collapse dynamics. https://arxiv.org/abs/2512.12862

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