Semi-Device-Independent Framework Based on Restricted Distrust in Prepare-and-Measure Experiments

Area of Science:

• Quantum Information Science
• Device-Independent Quantum Information

Background:

• Prepare-and-measure experiments are fundamental in quantum information.
• Existing frameworks often assume ideal device performance, limiting practical applications.
• The need for robust protocols tolerating imperfect quantum devices is critical.

Purpose of the Study:

• To develop a semi-device-independent framework for prepare-and-measure experiments.
• To allow tunable distrust in the performance of quantum devices.
• To explore quantum correlations, state discrimination, and random number generation under realistic conditions.

Main Methods:

• Introduced a framework where device characterization is not fully assumed.
• Defined a sender operating a preparation device with bounded fidelity.
• Defined a receiver operating an uncharacterized measurement device.
• Investigated quantum correlations without assuming Hilbert space dimension.

Main Results:

• Bounded the set of quantum correlations from interior and exterior.
• Derived optimal quantum state discrimination with bounded distrust.
• Applied results to certify detection efficiency.
• Demonstrated quantum-over-classical advantages and explored compatible distrust levels.
• Developed efficient semi-device-independent random number generation schemes.

Conclusions:

• The proposed framework offers a practical approach to quantum information processing with imperfect devices.
• Semi-device-independent protocols can certify device performance and enable secure applications like random number generation.
• The study bridges the gap between theoretical quantum advantages and real-world experimental limitations.