We present a systematic simple method for constructing deterministic remote
operations on single and multiple systems of arbitrary discrete dimensionality.
These operations include remote rotations, remote interactions and
measurements. The resources needed for an operation on a two-level system are
one ebit and a bidirectional communication of two cbits, and for an n-level
system, a pair of entangled n-level particles and two classical ``nits''. In
the latter case, there are n−1 possible distinct operations per one n-level
entangled pair. Similar results apply for generating interaction between a pair
of remote systems and for remote measurements. We further consider remote
operations on N spatially distributed systems, and show that the number of
possible distinct operations increases here exponentially, with the available
number of entangled pairs that are initial distributed between the systems. Our
results follow from the properties of a hybrid state-operator object
(``stator''), which describes quantum correlations between states and
operations.Comment: 18 pages, 3 figures, typo correction
