Efficient Approximation of Quantum Channel Capacities

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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} }

2021-11-22T13:51:34Z Sutter, Tobias Sutter, David Renner, Renato 2021-11-22T13:51:34Z 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<sup>3</sup>log(N)<sup>1/2</sup> ε <sup>-1</sup> ) 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. Efficient Approximation of Quantum Channel Capacities Sutter, David Mohajerin Esfahani, Peyman 2016 Sutter, Tobias Renner, Renato terms-of-use eng Mohajerin Esfahani, Peyman

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