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

TL;DR

This paper discusses potential failures in quantum tomography due to source drift and errors, proposing a method using Akaike's Information Criterion to detect such issues, especially when future measurements differ from the initial set.

Contribution

It introduces a practical approach to identify when quantum tomography assumptions break down, addressing challenges in applying classical model selection criteria to quantum data.

Findings

AIC can be adapted to quantum tomography for failure detection

Source drift and measurement differences can invalidate standard tomography

Proposed method improves reliability of quantum state estimation

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 Akaike's Information Criterion (AIC). 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.