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

—

Years open

—

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