Quantum state tomography in the real world: the search for rigor by an increasingly confused experimentalist

Abstract

The basic principles of quantum state tomography were first outlined by Stokes for the context of light polarisation more than 150 years ago. For an experimentalist the goal is clear: to use a series of measurement outcomes to make the best possible estimate of a system\'s quantum state, including phase information, with the least amount of measurement (and analysis) time and, if possible, also the least expensive and complicated apparatus. However, although the general ideas are straightforward, there is still much flexibility of choice in the practical details of how to implement tomography in the laboratory - details which may substantially influence the tomographic performance. For example, how do I make my measurements? How do I analyse my data? How confident can I be of my reconstruction anyway? Say, for example, I\'ve made my measurements and taken my data and I\'m now faced with two different ways, essentially equivalent at first glance, of analysing my data, where one way gives me \'better numbers\', e.g., a state with higher entanglement. Which do I choose? One may lead to a higher chance of a successful publication, but this is hardly a satisfactory way of making the decision. The perspective of an experimentalist motivates a fairly pragmatic approach to choosing the best technique for performing tomography. Does it work? How well? Can it work better? In this talk, I will use this approach and discuss issues which arise at each stage of the tomography process, using both numerical and real lab data to characterise the performance quality.