EURO 2024 Copenhagen
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2525. Efficient Quantum Relative Entropy Programming with SDP Preprocessing

Invited abstract in session TD-38: Semidefinite Programming and implementations, Quantum Information Theory and other applications, stream Conic Optimization: Theory, Algorithms, and Applications.

Tuesday, 14:30-16:00
Room: 34 (building: 306)

Authors (first author is the speaker)

1. Mehdi Karimi
Mathematics, Illinois State University
2. Levent Tuncel
Dept. of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo

Abstract

Optimization over the quantum relative entropy (QRE) cone has many applications in quantum information processing, for example, calculating the key rates for quantum key distribution (QKD) protocols. Recently, a new version of our convex optimization software package Domain-Driven Solver (DDS) was released with modified numerical approaches for solving QRE programming problems, potentially combined with many other convex function/set constraints. In this talk, we propose a preprocessing and two-phase approach for QRE programming to reduce the size and improve the conditioning of a given instance. Phase-I of this two-phase approach is a well-behaved convex optimization problem, such as minimizing a self-concordant barrier or an SDP. The reformulated QRE programming problem can be solved more efficiently and faster by DDS or other optimization algorithms. We finish the talk by presenting numerical results of using DDS for solving many classes of problems, including calculating the QKD rate for different protocols.

Keywords

Status: accepted

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