Efficient Experimental Qudit State Estimation via Point Tomography

TL;DR

This paper introduces point tomography with Fisher-symmetric measurements for efficient qudit state estimation, demonstrating near-optimal precision in a photonic experiment with reduced measurement outcomes.

Contribution

It presents a new measurement scheme that reduces outcomes for high-dimensional state estimation and experimentally validates its effectiveness with photonic qudits.

Findings

Achieved near-Gill-Massar limit precision with fewer measurement outcomes.

Reduced measurement outcomes from ~4d-3 to 2d-1 for state reconstruction.

Experimental demonstration with 4-dimensional quantum states.

Abstract

Point tomography is a new approach to the problem of state estimation, which is arguably the most efficient and simple method for modern high-precision quantum information experiments. In this scenario, the experimenter knows the target state that their device should prepare, except that intrinsic systematic errors will create small discrepancies in the state actually produced. By introducing a new kind of informationally complete measurement, dubbed Fisher-symmetric measurements, point tomography determines deviations from the expected state with optimal efficiency. In this method, the number of outcomes of a measurement saturating the Gill-Massar limit for reconstructing a $d$-dimensional quantum states can be reduced from $\sim 4d-3$ to only $2d-1$ outcomes. Thus, providing better scalability as the dimension increases. Here we demonstrate the experimental viability of point tomography. Using a modern photonic platform constructed with state-of-the-art multicore optical fiber technology, we generate 4-dimensional quantum states and implement seven-outcome Fisher-symmetric measurements. Our experimental results exhibit the main feature of point tomography, namely a precision close to the Gill-Massar limit with a single few-outcome measurement. Specifically, we achieved a precision of $3.8/N$ while the Gill-Massar limit for $d=4$ is $3/N$ ($N$ being the ensemble size).