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  • A. Winter
  • 2005
The inverse of Maurer's secret key distillation problem from (many independent realisations of) a triple of random variables X, Y, Z by two players (Alice and Bob) against an eavesdropper (Eve) is considered: the formation of the joint distribution (up to local degrading of Z) from secret key and public communication. We determine the asymptotically minimal(More)
The relative entropy of two distributions of n random variables, and more generally of two n-party quantum states, is an important quantity exhibiting, for example, the extent to which the two distributions/states are different. The relative entropy of the states formed by restricting to a smaller number m of parties is always less than or equal to the(More)
Two measures of sensitivity to eavesdropping for alphabets of quantum states were recently introduced by Fuchs and Sasaki in quant-ph/0302092. These are the accessible fidelity and quantumness. In this paper we prove an important property of both measures: They are multiplicative under tensor products. The proof in the case of accessible fidelity shows a(More)
To establish a more flexible relationship between the original equipment manufacturer (OEM) and suppliers, the use of flexible contracts in embedded system design has been proposed and it has been shown that such contracts allow a division of risk which often leads to a mitigation of inefficiencies. But from the perspective of the OEM, such flexible(More)
3 +Ax + B be an elliptic curve over. For each prime p of good reduction for E (all but finitely many), let E p := E mod p denote the reduced curve and let a p := p + 1 − #E p (p) be the trace of Frobenius. By a theorem of Hasse, each normalized trace x p := a p / p is a real number in the interval [−2, 2]. The x p vary with p in an apparently unpredictable(More)
At the AWS 1999, I discussed work on the Hasse principle achieved during the previous decade. The present lectures are meant as an introduction to significant progress achieved during the last 5 years, in particular to work of The text, which in part uses some earlier notes of mine, is not in final form. It is mainly a survey, but an attempt has been made(More)
  • A. Winter
  • 2006
Summary form only given. Recently, after being open for almost a decade, a complete proof of the quantum channel coding theorem was given by Devetak, using a peculiar code construction described as `random CSS code'. Unlike in it's classical analogue, Shannon's channel coding, the code depends not only on a test source but also on the channel. Recently, M(More)
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