# Have you been using the wrong estimator? These guys bound average fidelity using this one weird trick von Neumann didn't want you to know

• Published in 2015
In the collections
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the experiment is running. We show numerically that these bounds are quite tight for relevant distributions of density matrices. We also show that the Bayesian mean estimator is ideal in the sense of performing close to the bound without requiring optimization. Our results hold for all finite dimensional quantum systems.

### BibTeX entry

@article{Ferrie2015,
abstract = {We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the experiment is running. We show numerically that these bounds are quite tight for relevant distributions of density matrices. We also show that the Bayesian mean estimator is ideal in the sense of performing close to the bound without requiring optimization. Our results hold for all finite dimensional quantum systems.},
author = {Ferrie, Christopher and Kueng, Richard},
month = {mar},
title = {Have you been using the wrong estimator? These guys bound average fidelity using this one weird trick von Neumann didn't want you to know},
url = {http://arxiv.org/abs/1503.00677 http://arxiv.org/pdf/1503.00677v2},
year = 2015,
archivePrefix = {arXiv},
eprint = {1503.00677},
primaryClass = {quant-ph},
urldate = {2015-03-26},
collections = {Attention-grabbing titles,Probability and statistics}
}