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arXiv:2607.25838

Bipartite Bound Information Exists

Jef Pauwels, Nicolas Gisin, Renato Renner

quant-phSubmitted Jul 28, 2026• Announced Jul 29, 2026• 0 citations

v1 · Jul 28, 2026 v2 · Sep 8, 2026

Abstract

Bound entanglement is an extreme irreversibility of quantum theory: certain states cost entanglement to create, yet no singlet can be distilled from them. Twenty-five years ago, Gisin and Wolf asked whether classical cryptography admits the same phenomenon. Are there correlations, shared by two parties and an eavesdropper, that cost secret bits to create although none can be extracted? We show that such bound information exists and give an explicit example, a distribution of two bits and a trit. The proof exploits a gap between two ways of comparing eavesdroppers: one can be better informed than another in every mutual-information comparison and nevertheless unable to simulate the other's data. We further prove that the distributions which motivated the conjecture, standard-basis measurements of bound-entangled qutrit states, are not themselves examples: a secret key is extractable from them whenever their creation costs any secrecy. Other measurements of their purifications, in contrast, do yield bound information, even for the separable states among them. The analogy is thus one of resources, not of individual states and their measurement outcomes.

Comments: 5 + 15 pages, 2 figures, 2 tables

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It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret correlations, then this state has to be entangled. These results prove the existence of a two-way connection between secret and quantum correlations in the process of preparation. They also imply that either it is possible to map any bound entangled state into a distillable probability distribution or bipartite bound information exists.

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