Estimating Purity and Entropy in Stabilizer State Experiments

TL;DR

This paper introduces a practical method to estimate the purity and entropy of graph states in quantum experiments using stabilizer measurements, avoiding the need for full-state tomography.

Contribution

It provides an analytical approach to bound the purity of graph states based on stabilizer measurements, simplifying experimental quantification.

Findings

The method yields bounds consistent with full-state tomography results.

It reduces measurement complexity from exponential to linear in the number of qubits.

The approach is applicable to real experimental data for graph states.

Abstract

Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of measurement settings growing exponentially with the number of constituents involved. Thus, full-state tomography becomes experimentally infeasible even for a moderate number of qubits. In this paper we present a method to estimate the purity of experimentally achieved graph states with simple measurements. The observables we consider are the stabilizers of the underlying graph. Then, we formulate the problem as: "What is the state with the least purity that is compatible with the measurement data?" We solve this problem analytically and compare the obtained bounds with results from full-state tomography for simulated data.