Convex conservation of von Neumann entropy implies unitarity or antiunitarity

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.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

arXiv:2608.29373 [quant-ph]

(or arXiv:2608.29373v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.29373 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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