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.
New Journal of Physics
- Pub Date:
- December 2015
- Quantum Physics;
- Mathematics - Statistics Theory
- These guys submitted v1 with a clickbait title. You probably could have guessed what happened next