By Pierre van Baal
Lawsuits of a NATO ASI and Isaac Newton Institute Workshop held in Cambridge, united kingdom, June 23-July four, 1997
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Additional resources for Confinement, duality, and nonperturbative aspects of QCD
If we apply these two error rates and Eq. 10 to the requirement p ≤ pmax it results in (q1 + q2 ) ≤ 4 pmax . Eve has the possibility to vary her probability q1 in a big range. In contrast if we use the constraint p1 , p2 ≤ pmax which has the same property as the single error rate constraint in a random noisy channel, Eve’s possibility to choose the probabilities is shortened with q1 , q2 ≤ 2 pmax . , q1 = 3 pmax , q2 = 0 is accepted when we measure only one error rate, but rejected by the detailed error measurement).
Thus, the rate in which Alice and Bob select the same base will increase. We will discuss this more precisely in Sect. 1. Finally, the communication between Alice and Bob on the quantum channel is finished. They now switch to the public channel. So far, Alice holds the two strings of length m containing her choice of base and value and Bob a string of length m containing his choice of bases and his measurement results of length gq · m. The smaller size is due to the loss on the quantum channel.
They proved that their protocol is ideal if and only if NP ⊆ BPP, which is a hypothesis. 36 M. Pivk With the fact that a ideal reconciliation protocol depends on a open question in complexity, which is unlikely to be true, we have to find another solution. In Sect. 1 (universal hashing) we had a similar problem. There we define a str ongly univer sal2 class of hash functions, where the size of this class becomes too large and unpractical. But just a small change of the probability on the theoretical bound makes these classes useful.