### Abstract

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

Article number | 012104 |

Number of pages | 15 |

Journal | Physical Review A |

Volume | 77 |

Issue number | 1 |

Early online date | 15 Jan 2008 |

DOIs | |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- quantum states
- purification
- channels
- antisymmetric states
- physics

### Cite this

*Physical Review A*,

*77*(1), [012104]. https://doi.org/10.1103/PhysRevA.77.012104

}

*Physical Review A*, vol. 77, no. 1, 012104. https://doi.org/10.1103/PhysRevA.77.012104

**Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states.** / Hayashi, Masahito; Markham, Damian; Murao, Mio; Owari, Masaki; Virmani, Shashank.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states

AU - Hayashi, Masahito

AU - Markham, Damian

AU - Murao, Mio

AU - Owari, Masaki

AU - Virmani, Shashank

PY - 2008

Y1 - 2008

N2 - We study various distance-like entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be permutation symmetric. This allows us to calculate the explicit values of various entanglement measures for symmetric and antisymmetric basis states, observing that antisymmetric states are generally more entangled. We use these results to obtain a variety of interesting ensembles of quantum states for which the optimal LOCC discrimination probability may be explicitly determined and achieved. We also discuss applications to the construction of optimal entanglement witnesses.

AB - We study various distance-like entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be permutation symmetric. This allows us to calculate the explicit values of various entanglement measures for symmetric and antisymmetric basis states, observing that antisymmetric states are generally more entangled. We use these results to obtain a variety of interesting ensembles of quantum states for which the optimal LOCC discrimination probability may be explicitly determined and achieved. We also discuss applications to the construction of optimal entanglement witnesses.

KW - quantum states

KW - purification

KW - channels

KW - antisymmetric states

KW - physics

U2 - 10.1103/PhysRevA.77.012104

DO - 10.1103/PhysRevA.77.012104

M3 - Article

VL - 77

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 - 1

M1 - 012104

ER -