Superqubits

TL;DR

This paper extends the concept of quantum bits to a supersymmetric framework, generalizing entanglement measures and state classifications using supergroups, which could deepen understanding of quantum entanglement in supersymmetric theories.

Contribution

It introduces a supersymmetric generalization of n quantum bits, extending entanglement groups and measures to supergroups, and characterizes super-GHZ states via superhyperdeterminants.

Findings

Super-GHZ states characterized by superhyperdeterminant.

Extension of entanglement measures to supersymmetric case.

Supergroup generalizations of local operations and entanglement groups.

Abstract

We provide a supersymmetric generalization of n quantum bits by extending the local operations and classical communication entanglement equivalence group [SU(2)]^n to the supergroup [uOSp(1|2)]^n and the stochastic local operations and classical communication equivalence group [SL(2,C)]^n to the supergroup [OSp(1|2)]^n. We introduce the appropriate supersymmetric generalizations of the conventional entanglement measures for the cases of $n=2$ and $n=3$. In particular, super-Greenberger-Horne-Zeilinger states are characterized by a nonvanishing superhyperdeterminant.