The structure of superqubit states

TL;DR

This paper explores the mathematical structure of superqubit states, introducing a supergroup framework to generate and analyze entangled states, extending quantum information theory into supersymmetric domains.

Contribution

It introduces the global unitary supergroup for n-superqubits and demonstrates how it can generate entangled states, extending the conventional qubit framework.

Findings

Defined the supergroup $ ext{UOSp}((3^n+1)/2 | (3^n-1)/2)$ for n-superqubits

Showed the supergroup contains a subgroup acting transitively on the n-qubit subspace

Generated entangled states from separable states using supergroup actions

Abstract

Superqubits provide a supersymmetric generalisation of the conventional qubit in quantum information theory. After a review of their current status, we address the problem of generating entangled states. We introduce the global unitary supergroup $\text{UOSp}((3^n+1)/2 | (3^n-1)/2)$ for an $n$-superqubit system, which contains as a subgroup the local unitary supergroup $[\text{UOSp}(2|1)]^n$. While for $4>n>1$ the bosonic subgroup in $\text{UOSp}((3^n+1)/2 | (3^n-1)/2)$ does not contain the standard global unitary group $\text{SU}(2^n)$, it does have an $\text{USp}(2^n)\subset\text{SU}(2^n)$ subgroup which acts transitively on the $n$-qubit subspace, as required for consistency with the conventional multi-qubit framework. For two superqubits the $\text{UOSp}(5|4)$ action is used to generate entangled states from the "bosonic" separable state $|00\rangle$.