On the impossibility of extracting classical randomness using a quantum computer

Yevgeniy Dodis, Renato Renner

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 px, in reality it might be observed with probability p′x ∈ [(1 -δ)px,p x], for some small δ > 0 (so that p⊥ = 1 - σx p′x ≤ δ).

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings
Pages204-215
Number of pages12
Volume4052 LNCS
DOIs
StatePublished - 2006
Event33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 - Venice, Italy
Duration: Jul 10 2006Jul 14 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4052 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other33rd International Colloquium on Automata, Languages and Programming, ICALP 2006
CountryItaly
CityVenice
Period7/10/067/14/06

Fingerprint

Quantum computers
Quantum Computer
Randomness
Quantum Computation
Measurement errors
Measurement Error
Imperfect
Encryption
Cryptography
Model

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Dodis, Y., & Renner, R. (2006). On the impossibility of extracting classical randomness using a quantum computer. In Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings (Vol. 4052 LNCS, pp. 204-215). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4052 LNCS). https://doi.org/10.1007/11787006_18

On the impossibility of extracting classical randomness using a quantum computer. / Dodis, Yevgeniy; Renner, Renato.

Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings. Vol. 4052 LNCS 2006. p. 204-215 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4052 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dodis, Y & Renner, R 2006, On the impossibility of extracting classical randomness using a quantum computer. in Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings. vol. 4052 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4052 LNCS, pp. 204-215, 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006, Venice, Italy, 7/10/06. https://doi.org/10.1007/11787006_18
Dodis Y, Renner R. On the impossibility of extracting classical randomness using a quantum computer. In Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings. Vol. 4052 LNCS. 2006. p. 204-215. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11787006_18
Dodis, Yevgeniy ; Renner, Renato. / On the impossibility of extracting classical randomness using a quantum computer. Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings. Vol. 4052 LNCS 2006. pp. 204-215 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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