Evidence-based certification of quantum dimensions

Abstract

Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and continuous variables that is fully evidence-based, relying solely on the experimental data collected and no other unjustified assumptions whatsoever. Using the Bayesian concept of relative belief, we take the effective dimension of the state as the smallest one such that the posterior probability is larger than the prior, as dictated by the data. The posterior probabilities associated with the relative-belief ratios measure the strength of the evidence provide by these ratios so that we can assess whether there is weak or strong evidence in favor or against a particular dimension. Using experimental data from spectral-temporal and polarimetry measurements, we demonstrate how to correctly assign Bayesian plausible error bars for the obtained effective dimensions. This makes relative belief a conservative and easy-to-use model-selection method for any experiment.

11 pages, 4 figures, companion article in arXiv:2406.03343

References in corpus (18)

• High-dimensional quantum communication: benefits, progress, and future challenges
• Testing the Hilbert space dimension
• Device-independent tests of classical and quantum dimensions
• Semi-device-independent security of one-way quantum key distribution
• A Quantum Pulse Gate based on Spectrally Engineered Sum Frequency Generation
• Diluted maximum-likelihood algorithm for quantum tomography
• A lower bound on the dimension of a quantum system given measured data
• Dimension witnesses and quantum state discrimination
• Knowledge and ignorance in incomplete quantum state tomography
• Quantum degrees of polarization
• Security of device-independent quantum key distribution protocols: a review
• Device-independent certification of high-dimensional quantum systems
• Objective Compressive Quantum Process Tomography
• Universal compressive characterization of quantum dynamics
• Maximally polarized states for quantum light fields
• Certifying dimension of quantum systems by sequential projective measurements
• Direct Measurement of Higher-Order Nonlinear Polarization Squeezing
• Relative-belief inference in quantum information theory

Cited by in corpus (2)

• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Relative-belief inference in quantum information theory