Bound Secrecy

One of the most fascinating early endeavours in quantum information theory was the discovery that pure bipartite quantum entanglement is a quantifiable resource. Thus, for instance, one can take many copies of the standard currency for bipartite pure entanglement, the singlet state, and create many copies of any other non-maximally entangled bipartite pure state. Similarly one can take many copies of a non-maximally entangled bipartite pure state and distill out copies of a singlet. The rates of these conversion processes is quantified by the Shannon entropy of one half of the non-maximally entangled state.
The situation, however, for mixed states is different. Here we find that there are states for which no pure entanglement can be distilled, but these mixed states are in fact entangled. These states are called bound entangled states because they require some pure entanglement in order to create them (thus the entanglement is bound into the mixed state.) Bound entangled states are strange beasts, being entangled, and yet not being able to be converted back to any sort of pure state entanglement currency.
One interesting use of a standard currency for bipartite pure state entanglement is in key generation. In these protocols, Alice and Bob distill noisy quantum states to obtain pure entangled states of some standard currency which can then be used to share a private key. Since an essential part of these protocols has been to distill pure entangled states, it seems, when you first think about it, that bound entangled states would not be useful for private key generation. However, this turns out to not be correct! Karol Horodecki, Michal Horodecki, Pawel Horodecki and Jonathan Oppenheim have shown (PRL 094, 160502 (2005), quant-ph/0309110) that one can obtain a secure key from bound entangled states! So, while bound entangled states often don’t like your standard non-bound entangled states, it turns out that for secret key generation, they are useful.