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Faithfulness and Sensitivity for Ancilla-Assisted Process Tomography.

Seok Hyung Lie1,2, Hyunseok Jeong1

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Summary
This summary is machine-generated.

We introduce a local variant of quantum channel faithfulness, completing a proof on its equivalence to Jamiołkowski map invertibility. This advances understanding of quantum channel characterization using specific quantum states.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Communication

Background:

  • Faithfulness of a bipartite quantum state is crucial for containing information about an unknown quantum channel.
  • The original proof by D'Ariano and Presti established sufficiency but not full equivalence between state faithfulness and Jamiołkowski map invertibility.

Purpose of the Study:

  • To extend the applicability and generality of quantum channel faithfulness by introducing a local variant.
  • To complete the proof of equivalence between faithfulness and Jamiołkowski map invertibility.
  • To explore the relationship between faithfulness and a new concept, sensitivity, for various quantum channels.

Main Methods:

  • Introduction of a local variant of faithfulness for quantum states.
  • Mathematical proof to establish necessity for the equivalence between faithfulness and Jamiołkowski map invertibility.
  • Characterization of faithfulness and sensitivity for classes including unital channels, random unitary operations, and unitary operations.

Main Results:

  • The study completes the proof by demonstrating the necessity of faithfulness for Jamiołkowski map invertibility.
  • Unexpected non-equivalence results were found between faithfulness and sensitivity for certain quantum channel subclasses.
  • It is shown that only two classes of quantum states are needed to characterize states as faithful or sensitive to subclasses of quantum channels.

Conclusions:

  • The introduction of local faithfulness broadens the scope of quantum channel characterization.
  • The completed proof provides a rigorous link between quantum state properties and channel invertibility.
  • The findings offer insights into the structure of quantum channels and simplify the characterization process.