1Institute for Quantum Computing, University of Waterloo, Canada
2School of Computer Science, University of Waterloo, Canada
3Canadian Institute for Advanced Research, Toronto, Canada
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Abstract
We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for convex optimization problems over the set of all quantum measurements of a given system having a fixed number of measurement outcomes are obtained as a special case. In the case of linear objective functions for measurement optimization problems, our conditions reduce to the well-known Holevo-Yuen-Kennedy-Lax measurement optimality conditions. We illustrate how our conditions can be applied to various state transformation problems having non-linear objective functions based on the fidelity, trace distance, and quantum relative entropy.
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[1] Leonardo Banchi, Jason Pereira, Seth Lloyd, and Stefano Pirandola, “Convex optimization of programmable quantum computers”, npj Quantum Information 6, 42 (2020).
[2] Leonardo Banchi, Jason Pereira, Seth Lloyd, and Stefano Pirandola, “Optimization and learning of quantum programs”, arXiv:1905.01318.
[3] Leonid Faybusovich and Cunlu Zhou, “Long-Step Path-Following Algorithm for Quantum Information Theory: Some Numerical Aspects and Applications”, arXiv:1906.00037.
[4] Álvaro M. Alhambra, Georgios Styliaris, Nayeli A. Rodriguez-Briones, Jamie Sikora, and Eduardo Martin-Martinez, “Fundamental limitations to local energy extraction in quantum systems”, arXiv:1902.02357.
[5] Sam Cree and Jamie Sikora, “A fidelity measure for quantum states based on the matrix geometric mean”, arXiv:2006.06918.
[6] Samuel S. Cree and Jonathan Sorce, “Geometric conditions for saturating the data processing inequality”, arXiv:2011.03473.
The above citations are from SAO/NASA ADS (last updated successfully 2021-05-01 07:19:56). The list may be incomplete as not all publishers provide suitable and complete citation data.
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