Gradient-based stopping rules for maximum-likelihood quantum-state tomography
Scott C. Glancy, Emanuel H. Knill, Mark Girard
When performing maximum likelihood quantum state tomography, one must find the quantum state that maximizes the likelihood for observed measurements on identically prepared systems, all having that quantum state. This optimization is usually performed with iterative algorithms. This paper provides a stopping criterion for halting such iterations. Using the concavity of the log-likelihood function, the stopping criterion places an upper bound on the ratio of the true maximum likelihood and the likelihood of the state of the current iteration. We also discuss how this bound can be used for some likelihood ratio tests.
New Journal of Physics
maximum likelihood, quantum tomography, stopping criterion