Coarse-graining in retrodictive quantum state tomography

TL;DR

This paper introduces a method for retrodictive quantum state tomography that effectively separates phase errors, using coarse-graining to significantly improve data processing speed with minimal fidelity loss.

Contribution

It presents a novel analysis of coarse-graining techniques in retrodictive quantum state tomography, demonstrating substantial speed gains with limited accuracy reduction.

Findings

Coarse-graining dramatically increases data processing speed.

Minimal fidelity loss observed with moderate coarse-graining.

Effective separation and removal of phase errors in quantum state reconstruction.

Abstract

Quantum state tomography 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. We consider 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 there is only one click per measurement outcome -- a feature having a drastically adverse effect on data-processing times. We provide a thorough analysis of coarse-graining under various reconstruction algorithms, finding dramatic increases in speed for only modest sacrifices in fidelity.