Faithfulness and Sensitivity for Ancilla-Assisted Process Tomography

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.