Directly Estimating Mixed-State Entanglement with Bell Measurement Assistance

TL;DR

This paper introduces a scalable, robust method for directly estimating mixed-state entanglement in quantum systems using Bell measurements, enhancing efficiency and noise resilience over previous techniques.

Contribution

It develops an unbiased estimator for mixed-state entanglement utilizing Bell measurements, extending randomized measurement schemes to multi-qubit systems with improved robustness.

Findings

The estimator is effective with few measurement outcomes.

Bell measurements improve robustness to noise.

More versatile measurement settings increase efficiency.

Abstract

Entanglement plays a fundamental role in quantum physics and information processing. Here, we develop an unbiased estimator for mixed-state entanglement in the few-shot scenario and directly estimate it using random unitary evolution in a photonic system. As a supplement to traditional projective measurements, we incorporate Bell measurements on qubit-pairs, enriching the previous randomized measurement scheme, which is no-go in this task with only local unitary evolution. The scheme is scalable to n-qubits via Bell measurements on qubit-pairs. The estimator can be derived directly from a few consecutive outcomes while exhibiting greater robustness to system errors and noise compared to schemes based on shadow estimation. We find that, under a fixed measurement resource, the way with more versatile measurement settings with fewer repeats per setting is more efficient. Our protocol and demonstration advance the direct characterization of quantum states in practice.