On the general constraints in single qubit quantum process tomography.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Measurement

Background:

• Quantum process tomography (QPT) is essential for characterizing quantum operations.
• Understanding both trace-preserving and non-trace-preserving processes is crucial for accurate quantum system analysis.
• Existing methods may not fully capture the nuances of experimental data fitting.

Purpose of the Study:

• To review and derive explicit constraints for single-qubit quantum process tomography.
• To provide deeper insights into the structure of the process matrix.
• To illustrate the application of these methods using qubit leakage error models.

Main Methods:

• Review of established single-qubit quantum process tomography techniques.
• Derivation of general constraints for fitting experimental data in quantum process tomography.
• Analysis of process matrices, including those derived from qubit leakage error models.

Main Results:

• Explicit forms of general constraints for fitting experimental data in quantum process tomography were derived.
• The derived constraints offer enhanced understanding of the process matrix structure.
• Illustrative examples demonstrate the practical application and interpretability of process matrices, particularly for leakage errors.

Conclusions:

• The derived constraints improve the accuracy and interpretability of single-qubit quantum process tomography.
• Process matrix analysis, especially concerning leakage errors, yields valuable insights into quantum system behavior.
• This work provides a more robust framework for characterizing quantum processes.