Coarse-graining in retrodictive quantum state tomography

Quantum state tomography (QST) is a combination of experimental and data-processing methods for complete characterisation of a quantum system. However, it often operates in the highly idealised scenario of assuming perfect measurements. The errors implied by such an approach are entwined with other imperfections relating to the information processing protocol or application of interest. Weconsider the problem of retrodicting the quantum state of a system, existing prior to the application of random but known phase errors, allowing those errors to be separated and removed. The continuously random nature of the errors implies that effective measurement operators are never repeated. This is a feature of many physical scenarios such as photonic cluster state generation and has a drastically adverse effect on data-processing times. Utilising state-of-the-art approaches to quantum state tomography, we describe a novel and effective method to account for these errors, resulting in improved reconstruction fidelities. Furthermore, we show how the use of 'coarse-graining' introduced in this work can substantially reduce the computation time in several maximum likelihood algorithms, for only modest sacrifices in fidelity.