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A constructive violation of additivity of minimum output von Neumann entropy
Abstract
We give an explicit non-random example of nonadditivity of minimum output von Neumann entropy. The proof uses a finite-dimensional construction which imitates free Haar unitary behavior. The same channel gives a violation of additivity for the minimum output Rényi-p entropy for any p∈[1,∞]. Additionally, given any p0>0 and g>0, we extend the construction to obtain an explicit non-random channel which has entropy gap ≥g uniformly over p∈[p0,∞].
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BibTeX
@misc{shou2026constructive,
title = {{A constructive violation of additivity of minimum output von Neumann entropy}},
author = {Laura Shou and Alexey V. Gorshkov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23946},
eprint = {2609.23946},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23946},
}
RIS
TY - UNPB
TI - A constructive violation of additivity of minimum output von Neumann entropy
AU - Laura Shou
AU - Alexey V. Gorshkov
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.23946
UR - https://arxiv.org/abs/2609.23946
AB - We give an explicit non-random example of nonadditivity of minimum output von Neumann entropy. The proof uses a finite-dimensional construction which imitates free Haar unitary behavior. The same channel gives a violation of additivity for the minimum output Rényi-p entropy for any p∈[1,∞]. Additionally, given any p_0>0 and g>0, we extend the construction to obtain an explicit non-random channel which has entropy gap ≥g uniformly over p∈[p_0,∞].
ER -