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January 25, 2026npj Quantum InformationOpen Access

Optimising the relative entropy under semidefinite constraints

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Authors

GKGereon KoßmannRSRené Schwonnek

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Overview

Finding optimal bounds for relative entropy in quantum states indicates improved key rate estimations in QKD.

Key Points

  • The research aims to minimize the relative entropy of two quantum states while maintaining semidefinite constraints.
  • Developed an efficient method for calculating upper and lower bounds of relative entropy.
  • Built on an integral representation of quantum relative entropy from recent literature.
  • Produced bounds through a sequence of semidefinite programs (SDPs) to ensure accuracy and efficiency.
  • Ensured provable sublinear convergence in the optimization process.
  • Obtained provable upper and lower bounds for relative entropy of quantum states.
  • Achieved reliable convergence rates during the optimization iterations.
  • Demonstrated efficient resource usage concerning SDP matrix dimensions.

Cite This Study

Koßmann et al. (2026) studied this question.

synapsesocial.com/papers/6975b2eafeba4585c2d6e5aehttps://doi.org/10.1038/s41534-026-01184-4
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