PreprintCC BY-SA 4.0arXiv
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)→ 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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BibTeX
@misc{underwood2026convex,
title = {{Convex conservation of von Neumann entropy implies unitarity or antiunitarity}},
author = {Nicolas G. Underwood and Jonte R. Hance},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29373},
eprint = {2608.29373},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29373},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Convex conservation of von Neumann entropy implies unitarity or antiunitarity
AU - Nicolas G. Underwood
AU - Jonte R. Hance
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29373
UR - https://arxiv.org/abs/2608.29373
AB - On the space of density matrices D(H), Kadison's theorem establishes that all invertible convex transformations K:D(H)→ 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.
ER -