Bipartite bound information exists

The problem asks whether bipartite classical correlations can contain secret information that costs secrecy to create but yields no asymptotic secret key. Acín and Gisin framed the question in 2005 through the connection between entanglement and secret correlations.

Known results

• Acín and Gisin (2005) showed that measurements on entangled states produce secret correlations and that secret correlations from quantum states imply entanglement, leaving either distillability from all bound-entangled states or classical bound information.
• The previously proposed bound-entangled qutrit measurements are not counterexamples: where formation costs secrecy, key remains distillable.

July 2026 explicit counterexample

A preprint gives a two-bit–one-trit distribution satisfying $S(X;Y\|Z)=0<I_{\rm form}(X;Y\mid Z)$, and even $S(X;Y\|Z)=0<I(X;Y{\downarrow}Z)\leq I_{\rm form}(X;Y\mid Z)$. It therefore establishes bipartite classical bound information and settles the existence question.

Current status (as of July 2026): The existence question is settled affirmatively by an explicit arXiv construction; the older qutrit-based candidate is not a counterexample.