Key Rate Available from Mismatched Measurements in the BB84 Protocol and the Uncertainty Principle

Ryutaroh MATSUMOTO  Shun WATANABE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.10   pp.2870-2873
Publication Date: 2008/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.10.2870
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Information Theory and Its Applications)
Category: Information Theory
Keyword: 
BB84,  mismatched measurement,  quantum key distribution,  

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Summary: 
We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the mismatched measurements. Our lower bound shows that we can extract a secret key from the mismatched measurements with certain quantum channels, such as the channel over which the Hadamard matrix is applied to each qubit with high probability. Moreover, the entropic uncertainty principle implies that one cannot extract the secret key from both matched measurements and mismatched ones simultaneously, when we use the standard information reconciliation and privacy amplification procedure.