Detecting entanglement of unknown continuous variable states with random measurements

TL;DR

This paper introduces a method for detecting entanglement in unknown continuous variable quantum states using random homodyne measurements and semidefinite programming, enhancing the ability to identify entanglement with minimal prior information.

Contribution

It develops new linear constraints for entanglement witnesses based on covariance matrices and applies semidefinite programming to optimize entanglement detection from random measurements.

Findings

Effective detection of entanglement in squeezed vacuum states

High efficiency in identifying entanglement with limited measurement data

Applicable to general unknown covariance matrices

Abstract

We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing the entanglement witnesses based on second moments, and use them in a semidefinite program providing the optimal entanglement test for given random measurements. We test the method on the class of squeezed vacuum states and study the efficiency of entanglement detection in general unknown covariance matrices.