###
**Novotny, Jaroslav ; Alber, Gernot ; Jex, Igor** (2010):

*Asymptotic Evolution of Random Unitary Operations.*

In: Central European Journal of Physics, 8 (6), pp. 1001-1014. DOI: 10.2478/s11534-010-0018-8,

[Article]

## Abstract

We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.

Item Type: | Article |
---|---|

Erschienen: | 2010 |

Creators: | Novotny, Jaroslav ; Alber, Gernot ; Jex, Igor |

Title: | Asymptotic Evolution of Random Unitary Operations |

Language: | German |

Abstract: | We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits. |

Journal or Publication Title: | Central European Journal of Physics |

Journal volume: | 8 |

Number: | 6 |

Divisions: | 20 Department of Computer Science |

Date Deposited: | 30 Dec 2016 20:23 |

DOI: | 10.2478/s11534-010-0018-8 |

Identification Number: | TUD-CS-2010-2450 |

Export: | |

Suche nach Titel in: | TUfind oder in Google |

Send an inquiry |

**Options (only for editors)**

Show editorial Details |