  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.
