### Abstract

Original language | English |
---|---|

Article number | 8355678 |

Pages (from-to) | 6917-6928 |

Number of pages | 12 |

Journal | IEEE Transactions on Information Theory |

Volume | 64 |

Issue number | 10 |

Early online date | 07 May 2018 |

DOIs | |

Publication status | Published - 01 Oct 2018 |

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### Cite this

*IEEE Transactions on Information Theory*,

*64*(10), 6917-6928. [8355678]. https://doi.org/10.1109/TIT.2018.2833466

}

*IEEE Transactions on Information Theory*, vol. 64, no. 10, 8355678, pp. 6917-6928. https://doi.org/10.1109/TIT.2018.2833466

**Complexity and capacity bounds for quantum channels.** / Levene, Rupert H.; Paulsen, Vern I.; Todorov, Ivan G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Complexity and capacity bounds for quantum channels

AU - Levene, Rupert H.

AU - Paulsen, Vern I.

AU - Todorov, Ivan G.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum channel requires to realise a given operator system as its non-commutative confusability graph. We describe quantum complexity as a generalised minimum semidefinite rank and, in the case of a graph operator system, as a quantum intersection number. The quantum complexity and a closely related quantum version of orthogonal rank turn out to be upper bounds for the Shannon zero-error capacity of a quantum channel, and we construct examples for which these bounds beat the best previously known general upper bound for the capacity of quantum channels, given by the quantum Lovasz theta number

AB - We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum channel requires to realise a given operator system as its non-commutative confusability graph. We describe quantum complexity as a generalised minimum semidefinite rank and, in the case of a graph operator system, as a quantum intersection number. The quantum complexity and a closely related quantum version of orthogonal rank turn out to be upper bounds for the Shannon zero-error capacity of a quantum channel, and we construct examples for which these bounds beat the best previously known general upper bound for the capacity of quantum channels, given by the quantum Lovasz theta number

U2 - 10.1109/TIT.2018.2833466

DO - 10.1109/TIT.2018.2833466

M3 - Article

VL - 64

SP - 6917

EP - 6928

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 10

M1 - 8355678

ER -