Self-testing nonprojective quantum measurements in prepare-and-measure experiments.

Area of Science:

• Quantum Information Science
• Quantum Measurement Theory

Background:

• Self-testing is the most rigorous method for certifying quantum systems.
• Nonprojective quantum measurements are crucial for advanced quantum information processing but challenging to verify.

Purpose of the Study:

• To develop and experimentally validate methods for self-testing nonprojective quantum measurements.
• To certify that an uncharacterized measurement device implements a desired nonprojective positive-operator valued measure (POVM).

Main Methods:

• Theoretical investigation of self-testing in a prepare-and-measure scenario with dimensional bounds.
• Development of robust methods for self-testing extremal qubit POVMs and certifying nonprojectivity.
• Experimental demonstration using photonic systems to validate theoretical predictions.

Main Results:

• Successful robust self-testing of extremal qubit POVMs.
• Experimental certification of implemented measurements as nonprojective, closely matching ideal three- and four-outcome qubit POVMs.
• Demonstration of a genuine four-outcome qubit POVM certification.

Conclusions:

• The developed methods are robust to noise, enabling practical applications in quantum device certification.
• This work advances semi-device-independent certification of quantum devices.
• Highlights the feasibility of verifying complex quantum measurement properties through self-testing.