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On the Impossibility of Extracting Classical Randomness Using a Quantum Computer

  • Yevgeniy Dodis
  • Renato Renner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4052)

Abstract

In this work we initiate the question of whether quantum computers can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it was observed [SV86, MP91, DOPS04] that classical computers are insufficient for either one of these tasks when all they have access to is a realistic imperfect source of randomness, such as the Santha-Vazirani source.

We answer this question in the negative, even in the following very restrictive model. We generously assume that quantum computation is error-free, and all the errors come in the measurements. We further assume that all the measurement errors are not only small but also detectable: namely, all that can happen is that with a small probability p  ⊥ δ the (perfectly performed) measurement will result in some distinguished symbol ⊥ (indicating an “erasure”). Specifically, we assume that if an element x was supposed to be observed with probability p x , in reality it might be observed with probability p x ′∈[(1–δ)p x ,p x ], for some small δ>0 (so that p  ⊥ = 1 – ∑ x p x ′ ≤δ).

Keywords

Quantum Computer Quantum Operation Impossibility Result Classical Randomness Distinguished Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yevgeniy Dodis
    • 1
  • Renato Renner
    • 2
  1. 1.New York UniversityUSA
  2. 2.University of CambridgeUK

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