Entanglement Detection with Rotationally Covariant Measurements -- From Compton Scattering to Lemonade

TL;DR

This paper develops a method for detecting quantum entanglement using rotationally covariant measurements, deriving explicit POVMs, and demonstrating practical applications including an experiment with lemonade as a detector.

Contribution

It introduces a POVM framework for rotationally symmetric measurements, including a novel entanglement certification method and an experimental demonstration with soft drinks.

Findings

Entanglement can be certified using rotationally covariant measurements.

Bell violations are impossible under these measurements, but EPR steering can be detected.

Lemonade-based detectors are feasible for entanglement detection.

Abstract

The accurate and efficient detection of quantum entanglement remains a central challenge in quantum information science. In this work, we study the detection of entanglement of polarized photons for measurement devices that are solely specified by rotational symmetry. We derive explicit positive operator valued measures (POVMs) showing that from a quantum information perspective any such setting is classified by one real measurable parameter r. In Particular, we give a POVM formulation of the Klein--Nishina formula for Compton scattering of polarized photons. We provide an SDP-based entanglement certification method that operates on the full measured statistics and gives tight bounds, also considering semi-device independent scenarios. Furthermore, we show that, while Bell violations are impossible with rotationally covariant measurements, EPR steering can still be certified under one-sided symmetry constraints. Finally, we present a rotationally covariant showcase experiment, analyzing the scattering of polarized optical light in a selection of soft drinks. Our results suggest that lemonade-based detectors are suitable for entanglement detection.