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Local certification of unitary operations.

Ryszard Kukulski1, Mateusz Stępniak2, Kamil Hendzel2

  • 1Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland.

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Summary

This study explores local certification for quantum channels, extending quantum hypothesis testing. Optimal strategies minimize errors without auxiliary systems, using only one-way classical communication.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Communication

Background:

  • Quantum channels are fundamental in quantum information processing.
  • Quantum hypothesis testing is crucial for verifying quantum operations.
  • Local certification extends these concepts to distributed quantum systems.

Purpose of the Study:

  • To analyze the local certification of unitary quantum channels.
  • To minimize type II error probability under a fixed type I error probability.
  • To investigate the role of entanglement and auxiliary systems in local certification.

Main Methods:

  • Analysis of quantum channels operating on product states.
  • Application of quantum hypothesis testing principles.
  • Connection to the product numerical range of unitary matrices.

Main Results:

  • The optimal local strategy for quantum channel certification does not require auxiliary systems.
  • A single round of one-way classical communication is sufficient for optimal local certification.
  • Local strategies are generally optimal but can fail in specific extremal cases compared to global strategies.

Conclusions:

  • Local certification of unitary quantum channels is achievable with minimal resources.
  • The findings offer insights into the limitations and capabilities of local quantum information processing.
  • Applications extend to the local certification of von Neumann measurements.