### Abstract

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

Pages | 472-489 |

Number of pages | 18 |

Journal | Quantum Information & Computation |

Volume | 12 |

Issue number | 5-6 |

Publication status | Published - 1 May 2012 |

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### Keywords

- fidelity matrices
- gram matrices
- Holevo quantity
- quantum ensembles

### Cite this

*Quantum Information & Computation*,

*12*(5-6), 472-489.

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*Quantum Information & Computation*, vol. 12, no. 5-6, pp. 472-489.

**Matrices of fidelities for ensembles of quantum states and the Holevo quantity.** / Fannes, M.; De Melo, F.; Roga, W.; Zyczkowski, K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Matrices of fidelities for ensembles of quantum states and the Holevo quantity

AU - Fannes, M.

AU - De Melo, F.

AU - Roga, W.

AU - Zyczkowski, K.

PY - 2012/5/1

Y1 - 2012/5/1

N2 - The entropy of the Gram matrix of a joint purification of an ensemble of K mixed states yields an upper bound for the Holevo information χ of the ensemble. In this work we combine geometrical and probabilistic aspects of the ensemble in order to obtain meaningful bounds for χ. This is done by constructing various correlation matrices involving fidelities between every pair of states from the ensemble. For K = 3 quantum states we design a matrix of root fidelities that is positive and the entropy of which is conjectured to upper bound χ. Slightly weaker bounds are established for arbitrary ensembles. Finally, we investigate correlation matrices involving multi-state correlations in relation to the Holevo quantity.

AB - The entropy of the Gram matrix of a joint purification of an ensemble of K mixed states yields an upper bound for the Holevo information χ of the ensemble. In this work we combine geometrical and probabilistic aspects of the ensemble in order to obtain meaningful bounds for χ. This is done by constructing various correlation matrices involving fidelities between every pair of states from the ensemble. For K = 3 quantum states we design a matrix of root fidelities that is positive and the entropy of which is conjectured to upper bound χ. Slightly weaker bounds are established for arbitrary ensembles. Finally, we investigate correlation matrices involving multi-state correlations in relation to the Holevo quantity.

KW - fidelity matrices

KW - gram matrices

KW - Holevo quantity

KW - quantum ensembles

UR - http://www.rintonpress.com/journals/qic/

M3 - Article

VL - 12

SP - 472

EP - 489

JO - Quantum Information & Computation

T2 - Quantum Information & Computation

JF - Quantum Information & Computation

IS - 5-6

ER -