Detecting entanglement in any measurement using quantum networks

TL;DR

This paper introduces a method to detect entanglement in any quantum measurement using quantum networks, enabling device-independent verification and demonstrating advantages in network quantum steering.

Contribution

It develops a framework for witnessing entanglement in composite quantum measurements and extends it to network scenarios, providing a new tool for quantum measurement analysis.

Findings

Entanglement witnesses can detect measurement entanglement without trusting the measurement device.

Any entangled measurement offers an advantage in network quantum steering.

Rank-one projective entangled measurements can be detected in a device-independent manner.

Abstract

Entanglement is a key resource to demonstrate quantum advantage over classical strategies. Entanglement in quantum states is one of the most well-explored areas in quantum physics. However, a rigorous approach to understanding and detecting entanglement in composite quantum measurements is lacking. In this work, we focus on composite quantum measurements and classify them into two classes: entangled and separable measurements. As done for quantum states, we define analogously a notion of witness that can be used to detect entanglement in composite quantum measurements. Here, one does not need to trust the measurement to witness its entanglement but must trust the quantum states. We then further extend this approach to show that any entangled measurement provides an advantage in network quantum steering without inputs, also known as swap steering. Consequently, this provides a way to witness entanglement in any quantum measurement in a one-sided device-independent way. Finally, we consider the star network scenario and show that any rank-one projective entangled quantum measurement gives a quantum advantage. Thus, one can detect the entanglement in any rank-one projective measurement in a device-independent way.