Gradient-based stopping rules for maximum-likelihood quantum-state tomography

Abstract

When performing maximum-likelihood quantum-state tomography, one must find the quantum state that maximizes the likelihood of the state given observed measurements on identically prepared systems. The optimization is usually performed with iterative algorithms. This paper provides a gradient-based upper bound on the ratio of the true maximum likelihood and the likelihood of the state of the current iteration, regardless of the particular algorithm used. This bound is useful for formulating stopping rules for halting iterations of maximization algorithms. We discuss such stopping rules in the context of determining confidence regions from log-likelihood differences when the differences are approximately chi-squared distributed.

9 pages, single column, 1 figure. Updated to accepted manuscript version. Now includes section headings and other small editorial changes

References in corpus (6)

• On the Measurement of Qubits
• Continuous-variable optical quantum state tomography
• Reliable Quantum State Tomography
• Quantum state tomography of an itinerant squeezed microwave field
• Diluted maximum-likelihood algorithm for quantum tomography
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• Joint Quantum-State and Measurement Tomography with Incomplete Measurements
• Confidence Polytopes in Quantum State Tomography
• Investigating Bias in Maximum Likelihood Quantum State Tomography
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• Theory and experiment for resource-efficient joint weak-measurement
• Quadrature Histograms in Maximum Likelihood Quantum State Tomography
• Theory of versatile fidelity estimation with confidence
• Self-consistent state and measurement tomography with fewer measurements