dorsal/arxiv
View SchemaDistillation of secret key and entanglement from quantum states
| Authors | Igor Devetak, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306078 |
| URL | https://arxiv.org/abs/quant-ph/0306078 |
| DOI | 10.1098/rspa.2004.1372 |
| Journal | Proc. R. Soc. Lond. A, vol 461, pp 207--235, 2005. |
Abstract
We study and solve the problem of distilling secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to achieve the "wire-tapper" bound, the difference of the mutual information Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way public communication. This result yields information--theoretic formulas for the distillable secret key, giving ``ultimate'' key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specialising our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one-way LOCC (local operations and classical communication) which is asymptotically optimal: in fact we prove the so-called "hashing inequality" which says that the coherent information (i.e., the negative conditional von Neumann entropy) is an achievable EPR rate. This result is well--known to imply a whole set of distillation and capacity formulas which we briefly review.
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"abstract": "We study and solve the problem of distilling secret key from quantum states\nrepresenting correlation between two parties (Alice and Bob) and an\neavesdropper (Eve) via one-way public discussion: we prove a coding theorem to\nachieve the \"wire-tapper\" bound, the difference of the mutual information\nAlice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way\npublic communication.\n This result yields information--theoretic formulas for the distillable secret\nkey, giving ``ultimate\u0027\u0027 key rate bounds if Eve is assumed to possess a\npurification of Alice and Bob\u0027s joint state.\n Specialising our protocol somewhat and making it coherent leads us to a\nprotocol of entanglement distillation via one-way LOCC (local operations and\nclassical communication) which is asymptotically optimal: in fact we prove the\nso-called \"hashing inequality\" which says that the coherent information (i.e.,\nthe negative conditional von Neumann entropy) is an achievable EPR rate.\n This result is well--known to imply a whole set of distillation and capacity\nformulas which we briefly review.",
"arxiv_id": "quant-ph/0306078",
"authors": [
"Igor Devetak",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1098/rspa.2004.1372",
"journal_ref": "Proc. R. Soc. Lond. A, vol 461, pp 207--235, 2005.",
"title": "Distillation of secret key and entanglement from quantum states",
"url": "https://arxiv.org/abs/quant-ph/0306078"
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