# Genuine Multipartite Entanglement in the $3$-Photon Decay of Positronium

## TL;DR

This paper investigates the multipartite entanglement properties of three-photon states resulting from ortho-positronium decay, revealing how entanglement persists under different spin states and mixing scenarios, with potential applications in medical imaging.

## Contribution

It demonstrates the presence and robustness of genuine multipartite entanglement in three-photon states from positronium decay, highlighting differences between entanglement types under various spin conditions.

## Key findings

- Genuine multipartite entanglement persists when positronium is in a definite spin state.
- Entanglement survives even when all spin states are mixed equally.
- Dicke-type entanglement remains, while GHZ-type vanishes under symmetrization.

## Abstract

The electron-positron annihilation into two photons is a standard technology in medicine to observe e.g. metabolic processes in human bodies. A new tomograph will provide the possibility to observe not only direct $e^+ e^-$ annihilations but also the $3$ photons from the decay of ortho-positronium atoms formed in the body. We show in this contribution that the three-photon state with respect to polarisation degrees of freedom depends on the angles between the photons and exhibits various specific entanglement features. In particular genuine multipartite entanglement, a type of entanglement involving all degrees of freedoms, is subsistent if the positronium was in a definite spin eigenstate. Remarkably, when all spin eigenstates are mixed equally, entanglement --and even stronger genuine multipartite entanglement-- survives. Due to a "\textit{symmetrization}" process, however, $Dicke$-type of entanglement remains whereas $GHZ$-type of entanglement vanishes. The survival of particular entanglement properties in the mixing scenario may make it possible to extract quantum information in form of distinct entanglement features, e.g., from metabolic processes in human bodies.