### Abstract

Language | English |
---|---|

Article number | 032309 |

Number of pages | 16 |

Journal | Physical Review A |

Volume | 83 |

Issue number | 3 |

DOIs | |

Publication status | Published - 14 Mar 2011 |

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### Keywords

- quantum computational devices
- quantum-state space
- simulation
- noise models

### Cite this

*Physical Review A*,

*83*(3), [032309]. https://doi.org/10.1103/PhysRevA.83.032309

}

*Physical Review A*, vol. 83, no. 3, 032309. https://doi.org/10.1103/PhysRevA.83.032309

**Generalized state spaces and nonlocality in fault-tolerant quantum-computing schemes.** / Ratanje, N.; Virmani, Shashank.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized state spaces and nonlocality in fault-tolerant quantum-computing schemes

AU - Ratanje, N.

AU - Virmani, Shashank

PY - 2011/3/14

Y1 - 2011/3/14

N2 - We develop connections between generalized notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli directions. By considering restricted measurements one can (by considering the dual positive operators) construct single-particle-state spaces that are different to the usual quantum-state space. This leads to a modified notion of entanglement that can be very different to the quantum version (for example, Bell states can become separable). We use this approach to develop alternative methods of classical simulation that have strong connections to the study of nonlocal correlations: we construct noisy quantum computers that admit operations outside the Clifford set and can generate some forms of multiparty quantum entanglement, but are otherwise classical in that they can be efficiently simulated classically and cannot generate nonlocal statistics. Although the approach provides new regimes of noisy quantum evolution that can be efficiently simulated classically, it does not appear to lead to significant reductions of existing upper bounds to fault tolerance thresholds for common noise models.

AB - We develop connections between generalized notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli directions. By considering restricted measurements one can (by considering the dual positive operators) construct single-particle-state spaces that are different to the usual quantum-state space. This leads to a modified notion of entanglement that can be very different to the quantum version (for example, Bell states can become separable). We use this approach to develop alternative methods of classical simulation that have strong connections to the study of nonlocal correlations: we construct noisy quantum computers that admit operations outside the Clifford set and can generate some forms of multiparty quantum entanglement, but are otherwise classical in that they can be efficiently simulated classically and cannot generate nonlocal statistics. Although the approach provides new regimes of noisy quantum evolution that can be efficiently simulated classically, it does not appear to lead to significant reductions of existing upper bounds to fault tolerance thresholds for common noise models.

KW - quantum computational devices

KW - quantum-state space

KW - simulation

KW - noise models

UR - http://www.scopus.com/inward/record.url?scp=79952663495&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.83.032309

DO - 10.1103/PhysRevA.83.032309

M3 - Article

VL - 83

JO - Physical Review A - Atomic, Molecular, and Optical Physics

T2 - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032309

ER -