The impossibility of nonsignaling privacy amplification
Abstract
Barrett, Hardy, and Kent have shown in 2005 that protocols for quantum key agreement exist the security of which can be proven under the assumption that quantum or relativity theory is correct. More precisely, this is based on the nonlocal behavior of certain quantum systems, combined with the nonsignaling postulate from relativity. An advantage is that the resulting security is independent of what (quantum) systems the legitimate parties' devices operate on: they do not have to be trusted. Unfortunately, the protocol proposed by Barrett et al. cannot tolerate any errors caused by noise in the quantum channel. Furthermore, even in the errorfree case it is inefficient: its communication complexity is Theta(1/epsilon) when forcing the attacker's information below epsilon, even if only a single key bit is generated. Potentially, the problem can be solved by privacy amplification of relativistic  or nonsignaling  secrecy. We show, however, that such privacy amplification is impossible with respect to the most important form of nonlocal behavior, and application of arbitrary hash functions.
 Publication:

arXiv eprints
 Pub Date:
 June 2009
 arXiv:
 arXiv:0906.4760
 Bibcode:
 2009arXiv0906.4760H
 Keywords:

 Quantum Physics
 EPrint:
 24 pages, 2 figures