aiqbench analysis
This paper presents a significant theoretical breakthrough in quantum information theory by providing an explicit, non-random counterexample to the additivity of minimum output von Neumann entropy. The construction, which mimics free Haar unitary behavior, simultaneously demonstrates violations for Rényi-$p$ entropy across the full range of $1 \le p \le \infty$. These findings refine our understanding of quantum channel capacities and the fundamental limits of information transmission in finite-dimensional systems.
A constructive violation of additivity of minimum output von Neumann entropy
arXiv:2609.23946v1 Announce Type: new 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 also gives a violation of additivity for the minimum output R\'enyi-$p$ entropy for any $1\le p\le\infty$.
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 also gives a violation of additivity for the minimum output Rényi-$p$ entropy for any $1\le p\le\infty$.
arXiv:2609.23946 [quant-ph]
(or arXiv:2609.23946v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.23946 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 136 words
Related coverage
Quantum Channels Defy Entropy Additivity, University of Waterloo Finds
Quantum Zeitgeist · Aug 26, 2026
Counterexamples to additivity of minimum output $p$-R\'enyi entropy of quantum channels for all $p\ge 0$
arXiv · Oct 6, 2026
Closed-Form Arbitrary-Gap R\'enyi Nonadditivity Above Any Positive Order via Direct Products of Free Groups and High-Girth Graphs
arXiv · Oct 6, 2026
Almost One Bit Violation of Minimum-Output R\'enyi Entropy Additivity Simultaneously at All Orders
arXiv · Sep 17, 2026