A no-go theorem for irreversibility along single-branch collapse dynamics

TL;DR

This paper proves a fundamental no-go theorem showing that, under certain conditions, quantum collapse dynamics cannot be genuinely irreversible along single branches, highlighting the conditions for quasi-reversibility.

Contribution

It establishes a structural no-go theorem for irreversibility in quantum collapse dynamics, linking information preservation to quasi-reversibility in finite-dimensional systems.

Findings

Existence of topologically closed, forward-invariant subsets of the state space

Any two states in these subsets can be connected with arbitrary precision

Genuine irreversibility requires information erasure or non-compactness

Abstract

We study finite dimensional quantum systems with arbitrary collapse events, establishing, under no-information-erasure conditions, a structural no-go for operational irreversibility along single branches of the collapse dynamics. More precisely, we prove that, for every physically admissible selector of the collapse dynamics, there exists a topologically closed, forward-invariant subset of the projective state space on 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 a realized branch of outcomes guarantees islands of quasi-reversibility, while genuine irreversibility requires additional ingredients such as non-compactness or information erasure. KEYWORDS: Quantum collapse dynamics; Quasi-reversibility; Chain-recurrence; Information non-erasure.