Detecting entanglement and nonlocality with minimum observable length

TL;DR

This paper introduces the concept of detection length as a metric for verifying quantum entanglement and nonlocality, providing analytical models and semidefinite programming methods to optimize detection strategies and robustness.

Contribution

It extends the detection length framework to various quantum phenomena and develops tailored entanglement witnesses and Bell inequalities for minimal detection lengths.

Findings

Shorter detection length witnesses can be more noise-robust

Analytical models for detection lengths across entanglement types

Semidefinite programming constructs optimal witnesses

Abstract

Quantum entanglement and nonlocality are foundational to quantum technologies, driving quantum computation, communication, and cryptography innovations. To benchmark the capabilities of these quantum techniques, efficient detection and accurate quantification methods are indispensable. This paper focuses on the concept of "detection length" -- a metric that quantifies the extent of measurement globality required to verify entanglement or nonlocality. We extend the detection length framework to encompass various entanglement categories and nonlocality phenomena, providing a comprehensive analytical model to determine detection lengths for specified forms of entanglement. Furthermore, we exploit semidefinite programming techniques to construct entanglement witnesses and Bell's inequalities tailored to specific minimal detection lengths, offering an upper bound for detection lengths in given states. By assessing the noise robustness of these witnesses, we demonstrate that witnesses with shorter detection lengths can exhibit superior performance under certain conditions.