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3359. Optimization of the Relative Entropy under linear constraints via semidefinite programming

Invited abstract in session MD-42: Optimization in Quantum Information, stream Quantum Computing Optimization.

Monday, 14:30-16:00
Room: 98 (building: 306)

Authors (first author is the speaker)

1. Rene Schwonnek
ITP, Leibniz University Hannover

Abstract

Optimizing the quantum relative entropy under linear constraints is a central problem in Quantum Key Distribution (QKD) and other fields of (Quantum) Shannon theory. In particular providing provable lower and upper bounds is a highly relevant task.
We provide a practical and resource efficient method for this problem.
At the core of our work stands a recently described, and pleasingly elegant, integral representation of the quantum relative entropy, which we employ in order to formulate the problem of reliably bounding it as an iteration of semi definite programs (SDP).
In contrast to existing techniques, our method comes with a provable convergence guarantee of quadratic order, whilst staying resource efficient with the matrix dimension of the underlying SDPs. We furthermore can provide an estimate for the gap to the optimum at each stage of the iteration. Combining this with some clever heuristics for the iteration, we find that convergence can in practice be actually achieved much faster then theoretically guaranteed.

Keywords

Status: accepted

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