Joint Quantum-State and Measurement Tomography with Incomplete Measurements

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Metrology

Background:

• Accurate estimation of quantum states and measurements is fundamental for quantum information processing.
• Standard quantum tomography is susceptible to systematic errors arising from imperfect system knowledge.
• Existing methods require complex procedures and are prone to inaccuracies.

Purpose of the Study:

• To develop a procedure for simultaneous characterization of quantum states and measurements.
• To mitigate systematic errors inherent in standard quantum tomography.
• To provide a robust method applicable to state-of-the-art quantum systems.

Main Methods:

• Utilized a single high-fidelity state preparation and a limited set of high-fidelity unitary operations.
• Designed a novel experimental protocol and an optimization algorithm.
• Employed an iterative likelihood maximization approach for state and measurement estimation.

Main Results:

• Successfully mitigated systematic errors in quantum state and measurement characterization.
• Demonstrated the procedure's effectiveness on simulated data from a two-trapped-ion experiment.
• Developed a method using semi-definite programming to bound expectation values when unique state estimation is not possible.

Conclusions:

• The proposed procedure offers a more accurate and robust alternative to standard quantum tomography.
• The method is well-suited for current experimental quantum systems.
• Provides a framework for handling ambiguities in state estimation through bounding techniques.