Detecting entanglement of continuous variables with three mutually unbiased bases

TL;DR

This paper introduces an entanglement detection method for continuous variables using three mutually unbiased bases, employing an uncertainty relation and variance-based criterion, validated with photon pairs.

Contribution

It presents a novel entanglement criterion based on three mutually unbiased bases in continuous variables, expanding detection techniques.

Findings

Entangled photon pairs show correlations in three basis pairs.

The criterion effectively detects bipartite entanglement.

Uncertainty relation underpins the entanglement detection method.

Abstract

An uncertainty relation is introduced for a symmetric arrangement of three mutually unbiased bases in continuous variable phase space, and then used to derive a bipartite entanglement criterion based on the variance of global operators composed of these three phase space variables. We test this criterion using spatial variables of photon pairs, and show that the entangled photons are correlated in three pairs of bases.