Bipartite Bound Information Exists

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.

Source: arXiv:2607.25838v1 - http://arxiv.org/abs/2607.25838v1 PDF: https://arxiv.org/pdf/2607.25838v1 Original Link: http://arxiv.org/abs/2607.25838v1