Southwest Quantum Information and Technology

Partial quantum tomography using maximum likelihood estimation

Presenting Author: Adam Keith, NIST Boulder, CU Boulder
Contributing Author(s): Manny Knill, Scott Glancy

We present an algorithm to partially infer quantum states given histograms for both the observations of known reference states and an unknown quantum state. The tomography can be partial if the set of measurements is informationally incomplete, in which case not all features of the state are inferable. The reference histograms must be sufficient to resolve a given set of distinguishable subspaces and are drawn from mixtures of these subspaces with known probabilities. We use a maximum likelihood algorithm to infer both the POVM elements for the measurements and the density matrix of the unknown quantum state. We bin histograms to reduce the number of parameters that need to be inferred without losing much information. We discuss which quantities are fully inferable and what information can be reported for partially inferable quantities. Uncertainties of inferred quantities are obtained by parametric bootstrap resampling. Lastly, we present fidelity estimates for two and three ion symmetric qubit experiments, although this protocol is useful for many other systems.

(Session 5 : Thursday from 5:00 - 7:00 pm)