### 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 |

Pages | 204-215 |

Number of pages | 12 |

Volume | 4052 LNCS |

DOIs | |

State | Published - 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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - On the impossibility of extracting classical randomness using a quantum computer

AU - Dodis, Yevgeniy

AU - Renner, Renato

PY - 2006

Y1 - 2006

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=33746379606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746379606&partnerID=8YFLogxK

U2 - 10.1007/11787006_18

DO - 10.1007/11787006_18

M3 - Conference contribution

AN - SCOPUS:33746379606

SN - 3540359079

SN - 9783540359074

VL - 4052 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 204

EP - 215

BT - Automata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings

ER -