Publications Repository - Gdańsk University of Technology

In this paper, we develop a formalism for distilling aclassical key from a quantum state in a systematic way, expandingon our previous work on a secure key from bound entanglement(Horodecki et al., 2005). More detailed proofs, discussion, andexamples are provided of the main results. Namely, we demonstratethat all quantum cryptographic protocols can be recast in away which looks like entanglement theory, with the only changebeing that instead of distilling Einstein-Podolsky-Rosen (EPR)pairs, the parties distill private states. The form of these generalprivate states are given, and we show that there are a number ofuseful ways of expressing them. Some of the private states canbe approximated by certain states, which are bound entangled.Thus, distillable entanglement is not a requirement for a privatekey. We find that such bound entangled states are useful for acryptographic primitive we call a controlled private quantumchannel (PQC). We also find a general class of states, which havenegative partial transpose (are NPT), but which appear to bebound entangled. The relative entropy distance is shown to be anupper bound on the rate of a key. This allows us to compute theexact value of a distillable key for a certain class of private states.

Authors

• Karol Horodecki,
• Michał Horodecki,
• prof. dr hab. Paweł Horodecki link open in new tab ,
• Jonathan Oppenheim