Cite this problem as **Problem 24**.

**Problem**

Can all bipartite entangled states be used to generate secrete keys?

**Partial Results**

- In [1] it is shown that some bound entangled states do allow the extraction of a secret key. This is an extreme counterexample to the idea that secret key is best generated from an entangled state by first distilling pure singlets, and using these to get the key. In principle, this provides a new distinction among bipartite states in those which allow key generation and those which do not. The problem asks whether this is really a new distinction
- [2] provides a one-way distillation protocol being able to distill secret key and EPR-Pairs.
- In [3] a class of bound entangled states with positiv key rates is provided. The smallest state of this kind is 4Ä4, which shows that peculiar security contained in bound entangled states does not need high dimensional systems. For distilling key the Devatak-Winter protocol [2] is used.
- In [4] a protocol is presented which enables two parties to extract from untrusted states an arbitrarily long and secure key, even though the amount of distillable entanglement of the untrusted states can be arbitrarily small.

**References**

[1] K. Horodecki, M. Horodecki, P. Horodecki, J. Oppenheim, quant-ph/0309110 (2003).

[2] I. Devetak, A. Winter,quant-ph/0306078 (2003).

[3] K. Horodecki, L. Pankowski, M. Horodecki, P. Horodecki, quant-ph/0506203 (2005).

[4] K. Horodecki, Debbie Leung, Hoi-Kwong Lo, J. Oppenheim, quant-ph/0510067 (2005).