Qubit, superqubit and squbit

TL;DR

This paper compares formalisms using nilpotent variables to describe qubits, superqubits, and squbits, highlighting differences based on variable commutativity and their implications for entanglement and generalization.

Contribution

It clarifies the use of commuting and anticommuting nilpotent variables in describing qubits and superqubits, and introduces squbits as a solution to superqubit issues.

Findings

Nilpotent commuting variables effectively describe qubits and entanglement.

Anticommuting variables are suitable for superqubits but have limitations.

Squbits address specific problems associated with superqubits.

Abstract

We analyze recently proposed formalisms which use nilpotent variables to describe and/or generalize qubits and notion of entanglement. There are two types of them distinguished by the commutativity and or anti-commutativity of basics variables. While nilpotent commuting variables suit the new description of the qubits and entanglement, the anticommuting do not, but they can be used to describe generalized objects - superqubits. A squbit, in the present context, is a version of superqubit introduced to cure some of problematic properties of the superqubit.