A non-distillability criterion for secret correlations

TL;DR

This paper introduces a computable criterion to determine when secret correlations cannot be distilled into a secret key, paralleling entanglement distillation criteria, and explores implications for bound information and resource usefulness.

Contribution

It presents the first criterion for non-distillability of secret correlations, potentially enabling the identification of bound information and revealing the resource nature of positive secrecy cost.

Findings

The criterion can certify non-distillability of secret correlations.

Distributions with positive secrecy cost may still increase secrecy content.

The criterion's effectiveness impacts understanding of bound information.

Abstract

Within entanglement theory there are criteria which certify that some quantum states cannot be distilled into pure entanglement. An example is the positive partial transposition criterion. Here we present, for the first time, the analogous thing for secret correlations. We introduce a computable criterion which certifies that a probability distribution between two honest parties and an eavesdropper cannot be (asymptotically) distilled into a secret key. The existence of non-distillable correlations with positive secrecy cost, also known as bound information, is an open question. This criterion may be the key for finding bound information. However, if it turns out that this criterion does not detect bound information, then, a very interesting consequence follows: any distribution with positive secrecy cost can increase the secrecy content of another distribution. In other words, all correlations with positive secrecy cost constitute a useful resource.