### 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 - σ^{x} p′_{x} ≤ δ).

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings |

Publisher | Springer Verlag |

Pages | 204-215 |

Number of pages | 12 |

ISBN (Print) | 3540359079, 9783540359074 |

DOIs | |

State | Published - Jan 1 2006 |

Event | 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 - Venice, Italy Duration: Jul 10 2006 → Jul 14 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4052 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 |
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Country | Italy |

City | Venice |

Period | 7/10/06 → 7/14/06 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings*(pp. 204-215). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4052 LNCS). Springer Verlag. https://doi.org/10.1007/11787006_18