Linking Entanglement Detection and State Tomography via Quantum 2-Designs

TL;DR

This paper introduces an efficient entanglement detection method using quantum 2-design measurements that improves detection capabilities and converges to full state tomography, applicable in device-independent scenarios.

Contribution

The authors propose a novel entanglement detection approach based on quantum 2-designs that enhances detection efficiency and integrates seamlessly with quantum state tomography.

Findings

Higher likelihood of detecting a broader set of entangled states with more detectors.

Method is twice as effective as standard witnesses, providing bounds on entanglement.

Applicable to measurement-device-independent quantum scenarios.

Abstract

We present an experimentally feasible and efficient method for detecting entangled states with measurements that extend naturally to a tomographically complete set. Our detection criterion is based on measurements from subsets of a quantum 2-design, e.g., mutually unbiased bases or symmetric informationally complete states, and has several advantages over standard entanglement witnesses. First, as more detectors in the measurement are applied, there is a higher chance of witnessing a larger set of entangled states, in such a way that the measurement setting converges to a complete setup for quantum state tomography. Secondly, our method is twice as effective as standard witnesses in the sense that both upper and lower bounds can be derived. Thirdly, the scheme can be readily applied to measurement-device-independent scenarios.