Evidence-Based Certification of Quantum Dimensions

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum State Characterization

Background:

• Efficient quantum information processing requires accurately describing quantum states within a minimal Hilbert space.
• Current methods often rely on assumptions beyond experimental data.
• Determining the effective dimension of quantum states is a key challenge.

Purpose of the Study:

• To introduce a general, evidence-based dimension-certification protocol for quantum states.
• To utilize Bayesian relative belief for determining effective dimension without unjustified assumptions.
• To provide a robust method for assessing evidence for or against specific dimensions.

Main Methods:

• Developed a dimension-certification protocol applicable to both discrete and continuous variable systems.
• Employed Bayesian relative belief to define effective dimension based on posterior and prior probabilities derived from data.
• Utilized spectral-temporal and polarimetry measurement data for validation.

Main Results:

• Demonstrated a fully evidence-based protocol relying solely on experimental data.
• Showcased the assignment of Bayesian plausible error bars for effective dimensions.
• Validated the protocol's effectiveness using real-world experimental data.

Conclusions:

• Relative belief offers a conservative and user-friendly model-selection method for quantum experiments.
• The protocol enhances the reliability of determining quantum state dimensions.
• This approach facilitates more efficient and accurate quantum information processing.