On Deriving a Basis for the Vector Space of Bounded Qudit Error Operators over $C^d$

TL;DR

This paper derives a basis of generalized Pauli matrices for the space of bounded operators on a d-dimensional quantum system, facilitating analysis of qudit errors and their application in quantum teleportation.

Contribution

It introduces a basis for the operator space on qudits, extending the Pauli matrix concept to higher dimensions, with applications in quantum error analysis and teleportation.

Findings

Established a basis for bounded operators on qudits

Demonstrated use in quantum teleportation of a single qudit

Enhanced understanding of qudit error structures

Abstract

We derive a basis for the vector space of bounded operators acting on a $d$-dimensional system Hilbert space $C^d$. In the context of quantum computation the basis elements are identified as the generalised Pauli matrices - the error generators. As an application, we show how such matrices are used in the teleportation a single qudit.