Last week, my advisor and I released our first paper together. It also happens to be the first I have ever written. The work, “Behavior of the Maximum Likelihood in Quantum State Tomography”, is available on the arXiv. The paper source file, as well some data files necessary to produce the figures, may be found on GitHub.
The key result of our work is to provide a replacement for the Wilks Theorem in predicting the expected value of the loglikelihood ratio statistic. In the figure below (Figure 3 in the paper), I show numerical data, the Wilks Theorem (solid line), and the results of our work (dashed lines). It’s clear the Wilks Theorem does a poor job of predicting the expected value, while our result does much better. However, our result depends on the rank of the true state , and breaks down when the dimension of the Hilbert space is comparable to it.
Check it out! If you find any typos or other issues, please let me know.
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