When quantum tomography goes wrong: drift of quantum sources and other errors

Abstract

The principle behind quantum tomography is that a large set of observations—many samples from a ‘quorum’ of distinct observables—can all be explained satisfactorily as measurements on a single underlying quantum state or process. Unfortunately, this principle may not hold. When it fails, any standard tomographic estimate should be viewed skeptically. Here we propose a simple way to test for this kind of failure using the Akaike information criterion. We point out that the application of this criterion in a quantum context, while still powerful, is not as straightforward as it is in classical physics. This is especially the case when future observables differ from those constituting the quorum.