  Of crucial importance to the development of quantum computing and information
has been the construction of a quantum operations formalism that admits a
description of quantum noise while simultaneously revealing the behavior of an
open quantum system. The operator-sum representation is such a formalism and
has provided a succinct description for set of bounded operators that act on a
finite dimensional quantum system. In this paper we derive a basis for the set
of bounded operators that act on a $d$-dimensional Hilbert space and we
illustrate how this basis set may be extended and identified with a set of
elements upon which the operator-sum representation rests.
