Recently I finished my latest work that has been done in collaboration with my wonderful supervisor and Oxford experimental team and I would like to use this post to advertise it a bit in general terms. You can read it in full at arXiv.
The past quantum state method relies on a simple assumption: since in practical experimental situations you would like to monitor your system continuously and collect as much data as possible it makes sense to condition your probability not only what happened to your system BEFORE the time t (that is any given time for which you would like to make you probability prediction), but also AFTER the time t. In other words you use both the PAST and the FUTURE (from the point of the time, t, you are interested in) to make a probability prediction. This might sound a little bit sci-fi but as in general in quantum reality it is nothing too fancy, you basically just need to modify the Born rule a bit. The method was first proposed here and we used this kind of reasoning to argue stuff about correlation functions and improve fidelity of the teleportation protocol.
Here we took on the challenge to improve the experimental readout of the single electron quantum dot as well as modify existing techniques for parameter estimation. As it turns out, for typical experimental parameters, we are able to remove most of the noise and we are able to find time of each tunnelling event with super high precision. In addition to that we modified the Baum-Welch parameter estimation method and combined it with good old Bayesian to estimate both coherent and incoherent parameters under the same footing. So if you like quantum dots or you are just interested in quantum measurement theory in general, please have a look!