Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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


Glancy, S. , Knill, E. and Girard, M. (2012), Gradient-based stopping rules for maximum-likelihood quantum-state tomography, New Journal of Physics (Accessed February 26, 2024)
Created September 18, 2012, Updated February 19, 2017