By Abhay Ashtekar

ISBN-10: 8870881431

ISBN-13: 9788870881431

Chosen issues on quantum gravity are handled emphasizing extra geometrical me- equipment and conceptual concerns than sensible research, perturbative expansions and computation of numbers, The lirst half offers with Asymptotic Quantization sheding gentle at the foundation of the Bondi-Meizner-Sachs team within the gravitational radiation conception. the second one half is dedicated to canonical quantization, which gives the de- designated quantum dynamics and enhances the in basic terms kinematic;)] asympotic descrip- description preset"!Led within the lirsf half.

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**Example text**

4 A reconciliation protocol R p is ideal if it is both optimal and efficient. Brassard and Salvail determined when their optimal protocol becomes ideal, using the univer sal2 class of hash function H3 [9]. 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.

If the tag with cost w1 does not match but the second does, there must be at least an error in the string of Bob. In the case that both tags do not match, she can assume that either Eve manipulates the messages or the shared keys of Alice and Bob are different. 17) to Bob. Again to avoid the man-in-the-middle attack, Alice must authenticate her message. With the same tag length gauth as Bob’s before, yielding an authentication cost of w4 = 4 · (gauth + log2 log2 g˜ EC ) · log2 g˜ EC . 18) After Bob has compared the tags of Alice with his ones they agree the authentication step for the error correction is complete.

Sci. 22(3), 265–279 (1981) 14, 15, 16, 17, 18, 19 10. : A single quantum cannot be cloned. Nature 299(5886), 802–803 (1982). 1038/299802a0. 1038/299802a0 13 Chapter 3 Quantum Key Distribution M. Pivk In this chapter a complete QKD protocol is presented, starting from the transmission via the quantum channel up to the communication over the public channel. The protocol described here is the BB84 protocol, named after Bennett and Brassard [5]. There are other protocols like the B92 protocol [3], the six-state protocol [8], the SARG protocol [19] and the Ekert protocol [10], which are not discussed here.

### Asymptotic quantization: based on 1984 Naples lectures by Abhay Ashtekar

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