# N-level ghost-spins and entanglement

## TL;DR

This paper generalizes ghost-spins to N-level systems, explores their symmetries and entanglement properties, and demonstrates positive entanglement entropy in correlated ghost-spin states.

## Contribution

It introduces N-level ghost-spin models with various symmetries and analyzes their entanglement properties, revealing positive entanglement entropy in correlated states.

## Key findings

- Existence of positive norm correlated ghost-spin states.
- Entanglement entropy is positive in these correlated states.
- Various N-level generalizations lead to different symmetry structures.

## Abstract

Ghost-spins, 2-level spin-like variables with indefinite norm have been studied in previous work. Here we explore various $N$-level generalizations of ghost-spins. First we discuss a flavoured generalization comprising $N$ copies of the ghost-spin system, as well as certain ghost-spin chains which in the continuum limit lead to 2-dim $bc$-ghost CFTs with $O(N)$ flavour symmetry. Then we explore a symplectic generalization that involves antisymmetric inner products, and finally a ghost-spin system exhibiting $N$ irreducible levels. We also study entanglement properties. In all these cases, we show the existence of positive norm "correlated ghost-spin" states in two copies of ghost-spin ensembles obtained by entangling identical ghost-spins from each copy: these exhibit positive entanglement entropy.