Experimental Estimation of Quantum State Properties from Classical Shadows

TL;DR

This paper demonstrates experimentally that classical shadow techniques can efficiently estimate properties of high-dimensional quantum states, outperforming traditional methods in fidelity estimation with fewer measurements.

Contribution

It provides the first experimental validation of classical shadow-based property estimation for high-dimensional quantum optical states.

Findings

Classical shadows outperform traditional state reconstruction in fidelity estimation.

The method requires fewer measurements for accurate property estimation.

Experimental results validate the efficiency of shadow tomography in high-dimensional systems.

Abstract

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here we provide an experimental demonstration of property estimation based on classical shadows proposed in [H.-Y. Huang, R. Kueng, J. Preskill. Nat. Phys. https://doi.org/10.1038/s41567-020-0932-7 (2020)] and study its performance in the quantum optical experiment with high-dimensional spatial states of photons. We show on experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.