Editing Full Quantum state tomography with Maximum Likelihood Estimation (section)

==Properties==

* '''Figure of merit''': Density Matrix of the quantum state
* Multiple copies of the quantum state are required in this method.
* <math>E_j</math> should be tomographically complete.
* This method is preferred over [matrix inversion] as that method in some cases produces results which are not valid. This issue occurs when not enough measurements are made. 
* This method is extremely resource intensive.
* State preparation and measurement errors are taken into consideration in this method. The measurement errors are tackled by increasing the accuracy of the measuring apparatus.
* Error from counting statistics can also occur which are reduced by performing the measurements on a larger ensemble.
* Drift error can occur either in the state produced or the efficiency of the detection system and it can constrain data collection time.
* In addition to the mentioned errors, each experimental implementation can have its own unique errors.
* We assume that the noise on the coincidence measurements has a Gaussian probability distribution.