Sharp Continuity Bound for Quantum Conditional Entropy

What is the optimal uniform continuity bound for quantum conditional entropy in trace distance, depending only on the dimension of the conditioned system? The sharp bound $h_2(\delta) + \delta \log(d^2 - 1)$ up to $\delta = 1 - d^{-2}$ , conjectured by Wilde, is proved.

Result: Proved
Status: Resolved
AI contribution: AI co-developed
Method: Argument
Field: Quantum information theory
Posed by: Mark M. Wilde
Year posed: 2019
Years open: 7y
Solved: 2026-07-27
Model: ChatGPT-5.6 Sol
Vendor: OpenAI
Collaborators: —
Verification: Unreviewed
Publication: Preprint
Significance: 10 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

The key proof idea, adapting the tight classical argument of Alhejji and Smith to the fully quantum setting, was developed with ChatGPT-5.6 Sol.

Verification

Five-author arXiv preprint. Not yet peer-reviewed.

Sources

PaperarXiv:2607.24687 - Sharp continuity of quantum conditional entropy
Problem recordWilde 2019 - Conjecture statement

Sharp Continuity Bound for Quantum Conditional Entropy

What the AI did

Verification

Sources

Discussion