By Mickelsson J.
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But, more errors provide Eve with more information, while Bob’s information gets lower. Hence, both information curves cross at a specific error rate D0 : √ 1 − 1/ 2 max ≈ 15% I(α, β) = I (α, ǫ) ⇐⇒ D = D0 ≡ 2 (68) Consequently, the security criteria against individual attacks for the BB84 protocol reads: √ 1 − 1/ 2 (69) BB84 secure ⇐⇒ D < D0 ≡ 2 (62) For QBERs larger than D0 no (one-way communication) error correction and privacy amplification protocol can provide Alice and Bob with a secret key immune against any individual attacks.
A complete picture of these connections is thus not yet available. Let us emphasize that nonlocality plays no direct role in QC. Indeed, generally, Alice is in the absolute past of Bob. Nevertheless, Bell inequality can be violated as well by space like separated events as by time like separated events. However, the independence assumption necessary to derive Bell inequality is justified by locality considerations only for space-like separated events. F. Connection to Bell inequality S ≡ E(a, b) + E(a, b′ ) + E(a′ , b) − E(a′ , b′ ) ≤ 2 √ 1 − 1/ 2 .
Let us immediately stress that the complete analysis of eavesdropping on quantum channel is by far not yet finished. In this chapter we review some of the problems and solutions, without any claim of mathematical rigor nor complete cover of the huge and fast evolving literature. The general objective of eavesdropping analysis is to find ultimate and practical proofs of security for some quantum cryptosystems. Ultimate means that the security is guaranteed against entire classes of eavesdropping attacks, even if Eve uses not only the best of today’s technology, but any conceivable technology of tomorrow.