  The quantum equivalence principle says that, for any given point, it is
possible to find a quantum coordinate system with respect to which we have
definite causal structure in the vicinity of that point. It is conjectured that
this principle will play a similar role in the construction of a theory of
Quantum Gravity to the role played by the equivalence principle in the
construction of the theory of General Relativity.
  To actually implement the quantum equivalence principle we need a suitable
notion of quantum coordinate systems - setting up a framework for these is the
main purpose of the present paper. First we introduce a notion of extended
states consisting of a superposition of terms (labeled by $u$) where each term
corresponds to a manifold, $\mathcal{M}_u$, with fields defined on it. A
quantum coordinate system consists of an identification of points between some
subsets, $\mathcal{O}_u\subseteq \mathcal{M}_u$, of these manifolds along with
a coordinate, $x$, that takes the same value on those points identified.
  We also introduce a notion of quantum coordinate transformations (which can
break the identification map between the manifolds) and show how these can be
used to attain definite causal structure in the vicinity of a point.
  We discuss in some detail how the quantum equivalence principle might form a
starting point for an approach to constructing a theory of Quantum Gravity that
is analogous to way the equivalence principle is used to construct General
Relativity.
