Detecting entanglement from macroscopic measurements of the electric field and its fluctuations

TL;DR

This paper introduces a new family of entanglement witnesses based on macroscopic electric field measurements, enabling detection of entanglement in large quantum systems without full state tomography.

Contribution

It presents a novel, experimentally accessible method for detecting entanglement in open quantum systems using electric field quadratures and fluorescence, surpassing previous spin-squeezing inequalities.

Findings

Detects entanglement from almost any observation direction.

Applicable to various quantum emitters like atoms, ions, and superconducting qubits.

Effective for large, collective quantum states.

Abstract

To address the outstanding task of detecting entanglement in large quantum systems, entanglement witnesses have emerged, addressing the separable nature of a state. Yet optimizing witnesses, or accessing them experimentally, often remains a challenge. We here introduce a family of entanglement witnesses for open quantum systems, based on the electric field -- its quadratures and the total fluorescence. More general than spin-squeezing inequalities, it can detect new classes of entangled states, as changing the direction for far-field observation opens up a continuous family of witnesses, without the need for a state tomography. Their efficiency is demonstrated by detecting, from almost any direction, the entanglement of collective single-photon states, such as long-lived states generated by cooperative spontaneous emission. Able to detect entanglement in large quantum systems, these electric-field-based witnesses can be used on any set of emitters described by the Pauli group, such as atomic systems (cold atoms and trapped ions), giant atoms, color centers, and superconducting qubits.