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Computation of the smooth max-mutual information via semidefinite programming.

Christopher Popp1, Tobias C Sutter1, Beatrix C Hiesmayr1

  • 1Faculty of Physics, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria.

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We developed a new semidefinite programming algorithm to calculate quantum smooth max-mutual information for quantum states. This method offers accurate results or reliable upper bounds for quantum information processing tasks.

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Quantum informationSemidefinite programmingSmooth max-mutual informationSmooth max-relative entropy

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Area of Science:

  • Quantum Information Theory
  • Quantum Computing
  • Mathematical Physics

Background:

  • Quantum information theory quantifies information in quantum systems.
  • Smooth max-mutual information is a key measure for quantum correlations.
  • Efficient computation of these measures is crucial for quantum information processing.

Purpose of the Study:

  • To present an iterative algorithm for computing quantum smooth max-mutual information.
  • To extend semidefinite programming (SDP) techniques in quantum information theory.
  • To provide a method for bounding the one-shot distillable key of quantum states.

Main Methods:

  • An iterative algorithm based on semidefinite programming (SDP).
  • Development and analysis of novel primal and dual SDP formulations.
  • Proof of strong duality for the proposed SDP.

Main Results:

  • The algorithm accurately computes quantum smooth max-mutual information under a specific rank condition.
  • It provides a reliable upper bound when the rank condition is not met.
  • The method is applicable to bipartite quantum states in any dimension.

Conclusions:

  • The developed SDP-based algorithm enhances the computation of quantum information measures.
  • This work extends SDP applications in quantum information theory.
  • The findings improve capabilities for various quantum information processing tasks.