Bounding the fidelity of quantum many-body states from partial information

TL;DR

This paper introduces an algorithm to estimate the fidelity of quantum many-body states using limited measurement data, especially effective for permutationally invariant states in experimental settings.

Contribution

It provides a novel method to lower bound fidelity from partial information, tailored for permutationally invariant states and applicable to real experiments with noise and partial symmetry.

Findings

Can certify high-fidelity spin squeezed states with minimal measurements

Accounts for measurement noise and partial symmetry in fidelity estimation

Demonstrates practical applicability in atomic ensemble experiments

Abstract

We formulate an algorithm to lower bound the fidelity between quantum many-body states only from partial information, such as the one accessible by few-body observables. Our method is especially tailored to permutationally invariant states, but it gives nontrivial results in all situations where this symmetry is even partial. This property makes it particularly useful for experiments with atomic ensembles, where relevant many-body states can be certified from collective measurements. As an example, we show that a $\xi^2\approx-6\;\text{dB}$ spin squeezed state of $N=100$ particles can be certified with a fidelity up to $F=0.999$, only from the measurement of its polarization and of its squeezed quadrature. Moreover, we show how to quantitatively account for both measurement noise and partial symmetry in the states, which makes our method useful in realistic experimental situations.