dorsal/arxiv
View SchemaGeneral paradigm for distilling classical key from quantum states
| Authors | Karol Horodecki, Michal Horodecki, Pawel Horodecki, Jonathan Oppenheim |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506189 |
| URL | https://arxiv.org/abs/quant-ph/0506189 |
| DOI | 10.1109/TIT.2008.2009798 |
| Journal | IEEE Trans. Inf. Theory 55, 1898 (2009) |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We develop a formalism for distilling a classical key from a quantum state in a systematic way, expanding on our previous work on secure key from bound entanglement [K. Horodecki et. al., Phys. Rev. Lett. 94 (2005)]. More detailed proofs, discussion and examples are provided of the main results. Namely, we demonstrate that all quantum cryptographic protocols can be recast in a way which looks like entanglement theory, with the only change being that instead of distilling EPR pairs, the parties distill private states. The form of these general private states are given, and we show that there are a number of useful ways of expressing them. Some of the private states can be approximated by certain states which are bound entangled. Thus distillable entanglement is not a requirement for a private key. We find that such bound entangled states are useful for a cryptographic primitive we call a controlled private quantum channel. We also find a general class of states which have negative partial transpose (are NPT), but which appear to be bound entangled. The relative entropy distance is shown to be an upper bound on the rate of key. This allows us to compute the exact value of distillable key for a certain class of private states.
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"abstract": "We develop a formalism for distilling a classical key from a quantum state in\na systematic way, expanding on our previous work on secure key from bound\nentanglement [K. Horodecki et. al., Phys. Rev. Lett. 94 (2005)]. More detailed\nproofs, discussion and examples are provided of the main results. Namely, we\ndemonstrate that all quantum cryptographic protocols can be recast in a way\nwhich looks like entanglement theory, with the only change being that instead\nof distilling EPR pairs, the parties distill private states. The form of these\ngeneral private states are given, and we show that there are a number of useful\nways of expressing them. Some of the private states can be approximated by\ncertain states which are bound entangled. Thus distillable entanglement is not\na requirement for a private key. We find that such bound entangled states are\nuseful for a cryptographic primitive we call a controlled private quantum\nchannel. We also find a general class of states which have negative partial\ntranspose (are NPT), but which appear to be bound entangled. The relative\nentropy distance is shown to be an upper bound on the rate of key. This allows\nus to compute the exact value of distillable key for a certain class of private\nstates.",
"arxiv_id": "quant-ph/0506189",
"authors": [
"Karol Horodecki",
"Michal Horodecki",
"Pawel Horodecki",
"Jonathan Oppenheim"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TIT.2008.2009798",
"journal_ref": "IEEE Trans. Inf. Theory 55, 1898 (2009)",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "General paradigm for distilling classical key from quantum states",
"url": "https://arxiv.org/abs/quant-ph/0506189"
},
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