Convex conservation of von Neumann entropy implies unitarity or antiunitarity

Nicolas G. Underwood; Jonte R. Hance

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arXiv · 2608.29373

Convex conservation of von Neumann entropy implies unitarity or antiunitarity

Nicolas G. Underwood·Jonte R. Hance

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Abstract

On the space of density matrices $D(H)$, Kadison's theorem establishes that all invertible convex transformations $K:D(H)\to D(H)$ are unitarity or antiunitary. For a finite Hilbert space, we propose a similar theorem which replaces the invertibility requirement with that of entropy conservation. Thus, we argue, the supposition of reversibility in quantum mechanics may be replaced with a principle of entropy conservation.

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Nicolas G. Underwood, Jonte R. Hance. 2026-08-29. Convex conservation of von Neumann entropy implies unitarity or antiunitarity. https://arxiv.org/abs/2608.29373

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