Quantum Tomography of Pure States with Projective Measurements Distorted by Experimental Noise

TL;DR

This paper compares two quantum state tomography methods using projective measurements affected by experimental noise, evaluating their accuracy in reconstructing pure qubit states with potential applications to higher dimensions.

Contribution

It introduces a comparison of SIC-POVM and MUB-based frames for noisy pure state estimation, demonstrating their effectiveness and potential for generalization.

Findings

Both frames achieve high fidelity in state reconstruction.

The MUB-based frame shows slightly better robustness to noise.

The methods are adaptable to higher-dimensional quantum systems.

Abstract

The article undertakes the problem of pure state estimation from projective measurements based on photon counting. Two generic frames for qubit tomography are considered -- one composed of the elements of the SIC-POVM and the other defined by the vectors from the mutually unbiased bases (MUBs). Both frames are combined with the method of least squares in order to reconstruct a sample of input qubits with imperfect measurements. The accuracy of each frame is quantified by the average fidelity and purity. The efficiency of the frames is compared and discussed. The method can be generalized to higher-dimensional states and transferred to other fields where the problem of complex vectors reconstruction appears.