CHSH Bell Tests For Optical Hybrid Entanglement

TL;DR

This paper demonstrates practical methods for verifying optical hybrid entanglement through CHSH Bell tests, enabling loophole-free quantum correlation verification with realistic detection efficiencies.

Contribution

It introduces two Bell test schemes suitable for hybrid entanglement verification that do not rely on postselection or fair-sampling assumptions.

Findings

Bell violation possible with >82% efficiency using photon number on/off detection

Parity measurements require 94% efficiency but work at higher photon numbers

Methods enable loophole-free tests with feasible experimental setups

Abstract

Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous and discrete variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the nature of this entanglement is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality tests, enabling practical verification of quantum correlations for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting, and to verification of hybrid entanglement in real-world applications.