Classifying, quantifying, and witnessing qudit-qumode hybrid entanglement

TL;DR

This paper classifies and analyzes hybrid entanglement between discrete-variable and continuous-variable quantum systems, providing a framework to distinguish different types and demonstrating the natural occurrence of true hybrid entanglement in practical scenarios.

Contribution

It introduces a classification scheme for hybrid entangled states, including pure, mixed, and truly hybrid states, and discusses methods for witnessing and quantifying entanglement.

Findings

True hybrid entanglement naturally occurs in physical settings.

The classification distinguishes states based on their Hilbert space support.

Entanglement witnessing and quantification methods are discussed.

Abstract

Recently, several hybrid approaches to quantum information emerged which utilize both continuous- and discrete-variable methods and resources at the same time. In this work, we investigate the bipartite hybrid entanglement between a finite-dimensional, discrete-variable quantum system and an infinite-dimensional, continuous-variable quantum system. A classification scheme is presented leading to a distinction between pure hybrid entangled states, mixed hybrid entangled states (those effectively supported by an overall finite-dimensional Hilbert space), and so-called truly hybrid entangled states (those which cannot be described in an overall finite-dimensional Hilbert space). Examples for states of each regime are given and entanglement witnessing as well as quantification are discussed. In particular, using the channel map of a thermal photon noise channel, we find that true hybrid entanglement naturally occurs in physically important settings. Finally, extensions from bipartite to multipartite hybrid entanglement are considered.