On Additivity Questions

Keiji Matsumoto

Peter W. Shor

In this paper, I discuss the additivity conjecture in quantum information theory.The additivity conjecture was originally a set of at least four conjectures.These conjectures said that certain functions of quantum states and channels were additive under tensor products.While some of these conjectures were previously known to be stronger than others, they have recently all been proved equivalent.This conjecture is a very intriguing mathematical question which the best efforts of a large number of quantum information theorists have not been able to resolve for nearly a decade.It is a mathematically elegant question that is one of the most important open questions in the field of quantum information and computation.This paper then is intended to be both an exposition of the conjecture, its background, and some of the methods that have been used to yield partial results for it, as well as a plea for help in resolving this conjecture.Very recently (summer 2007), substantial progress has been made on this conjecture, in that counterexamples to a set of stronger conjectures have been found.These will be described briefly.

Keiji Matsumoto

Mohamed Afane, Kayla Laufer, Wenqi Wei +4 more

Language models have become practical tools for quantum computing education and research, from summarizing technical papers to explaining theoretical concepts and answering questions about recent developments in the field. While existing benchmarks evaluate quantum code generation and circuit design, their understanding of quantum computing concepts has not been systematically measured. Quantum-Audit addresses this gap with 2,700 questions covering core quantum computing topics. We evaluate 26 models from leading organizations. Our benchmark comprises 1,000 expert-written questions, 1,000 questions extracted from research papers using LLMs and validated by experts, plus an additional 700 questions including 350 open-ended questions and 350 questions with false premises to test whether models can correct erroneous assumptions. Human participants scored between 23% and 86%, with experts averaging 74%. Top-performing models exceeded the expert average, with Claude Opus 4.5 reaching 84% accuracy, though top models showed an average 12-point accuracy drop on expert-written questions compared to LLM-generated ones. Performance declined further on advanced topics, dropping to 73% on security questions. Additionally, models frequently accepted and reinforced false premises embedded in questions instead of identifying them, with accuracy below 66% on these critical reasoning tasks.

PETER T. LANDSBERG, David John Morgan

Ralph Bottesch, Dmitry Gavinsky, Hartmut Klauck