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# Efficient Approximation of Quantum Channel Capacities

Type of Publication: | Journal article |

Publication status: | Published |

Author: | Sutter, David; Sutter, Tobias; Mohajerin Esfahani, Peyman; Renner, Renato |

Year of publication: | 2016 |

Published in: | IEEE Transactions on Information Theory ; 62 (2016), 1. - pp. 578-598. - IEEE. - ISSN 0018-9448. - eISSN 1557-9654 |

ArXiv-ID: | arXiv:1407.8202 |

DOI (citable link): | https://dx.doi.org/10.1109/TIT.2015.2503755 |

Summary: |
We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite-dimensional output under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To provide an additive ε-close estimate to the capacity, the presented algorithm requires O((N ν M)M
^{3}log(N)^{1/2} ε ^{-1} ) steps, where N denotes the input alphabet size and M denotes the output dimension. We then generalize the method to the task of approximating the capacity of classical-quantum channels with a bounded continuous input alphabet and a finite-dimensional output. This, using the idea of a universal encoder, allows us to approximate the Holevo capacity for channels with a finite-dimensional quantum mechanical input and output. In particular, we show that the problem of approximating the Holevo capacity can be reduced to a multi-dimensional integration problem. For certain families of quantum channels, we prove that the complexity to derive an additive ε-close solution to the Holevo capacity is subexponential or even polynomial in the problem size. We provide several examples to illustrate the performance of the approximation scheme in practice. |

Subject (DDC): | 004 Computer Science |

Refereed: | Yes |

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SUTTER, David, Tobias SUTTER, Peyman MOHAJERIN ESFAHANI, Renato RENNER, 2016. Efficient Approximation of Quantum Channel Capacities. In: IEEE Transactions on Information Theory. IEEE. 62(1), pp. 578-598. ISSN 0018-9448. eISSN 1557-9654. Available under: doi: 10.1109/TIT.2015.2503755

@article{Sutter2016Effic-55613, title={Efficient Approximation of Quantum Channel Capacities}, year={2016}, doi={10.1109/TIT.2015.2503755}, number={1}, volume={62}, issn={0018-9448}, journal={IEEE Transactions on Information Theory}, pages={578--598}, author={Sutter, David and Sutter, Tobias and Mohajerin Esfahani, Peyman and Renner, Renato} }