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.

Investigating Bias in Maximum Likelihood Quantum State Tomography



Scott C. Glancy, Hilma M. Vasconcelos, George B. Silva


Maximum likelihood quantum state tomography yields estimators that, in spite of the fact that they are consistent, may have bias. The bias of an estimator is the difference between the expected value of the estimate and the true value of the parameter being estimated. This paper investigates bias in the widely used maximum likelihood quantum state tomography. Our goal is to understand how the amount of bias depends on factors such as the purity of the true state, the number of measurements performed, and the number of different bases in which the system is measured. For that, we perform numerical experiments that simulate optical homodyne tomography under various conditions, perform tomography, and estimate bias in the purity of the estimated state. We find that estimates of higher purity states exhibit considerable bias, such that the estimates have lower purity than the true states.
Physical Review A (Atomic, Molecular and Optical Physics)


bias, maximum likelihood, quantum state tomography


Glancy, S. , Vasconcelos, H. and Silva, G. (2017), Investigating Bias in Maximum Likelihood Quantum State Tomography, Physical Review A (Atomic, Molecular and Optical Physics), [online], (Accessed July 23, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created February 8, 2017, Updated November 10, 2018