Practical Entanglement Estimation for Spin-System Quantum Simulators

TL;DR

This paper introduces practical methods for estimating entanglement in quantum simulators using accessible measurements, applicable to various platforms and robust against noise, aiding experimental studies and benchmarking.

Contribution

It proposes a simple observable-based scheme to bound entanglement and evaluates the effectiveness of standard measurements as entanglement witnesses in realistic conditions.

Findings

A single observable provides a lower bound to entanglement.

Standard measurements can serve as effective entanglement witnesses.

Methods are applicable to noisy, mixed states in experimental setups.

Abstract

We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focussing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and which may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the performance of routinely measured observables as quantitative entanglement witnesses. Possible applications include experimental studies of entanglement scaling in critical systems and the reliable benchmarking of quantum simulators.