Physical Underpinnings of Privacy

One of the remarkable features of quantum mechanics is the ability to ensure secrecy. Private states embody this effect, as they are precisely those multipartite quantum states from which two parties can produce a shared secret that cannot in any circumstance be correlated to an external system. Nat...

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Bibliographic Details
Published in:arXiv.org 2008-10
Main Authors: Renes, Joseph M, Jean-Christian Boileau
Format: Article
Language:English
Subjects:
Distillation
Error correcting codes
Error correction
Information theory
Privacy
Quantum cryptography
Quantum entanglement
Quantum mechanics
Quantum phenomena
Quantum theory
Online Access:Get full text
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Summary:One of the remarkable features of quantum mechanics is the ability to ensure secrecy. Private states embody this effect, as they are precisely those multipartite quantum states from which two parties can produce a shared secret that cannot in any circumstance be correlated to an external system. Naturally, these play an important role in quantum key distribution (QKD) and quantum information theory. However, a general distillation method has heretofore been missing. Inspired by Koashi's complementary control scenario (arXiv:0704.3661v1 [quant-ph]), we give a new definition of private states in terms of one party's potential knowledge of two complementary measurements made on the other and use this to construct a general method of private state distillation using quantum error-correcting codes. The procedure achieves the same key rate as recent, more information-theoretic approaches while demonstrating the physical principles underlying privacy of the key. Additionally, the same approach can be used to establish the hashing inequality for entanglement distillation, as well as the direct quantum coding theorem.
ISSN:2331-8422
DOI:10.48550/arxiv.0803.3096