  We consider the effects of local interactions upon quantum mechanically
entangled systems. In particular we demonstrate that non-local correlations
cannot increase through local operations on any of the subsystems, but that
through the use of quantum error correction methods, correlations can be
maintained. We provide two mathematical proofs that local general measurements
cannot increase correlations, and also derive general conditions for quantum
error correcting codes. Using these we show that local quantum error correction
can preserve nonlocal features of entangled quantum systems. We also
demonstrate these results by use of specific examples employing correlated
optical cavities interacting locally with resonant atoms. By way of counter
example, we also describe a mechanism by which correlations can be increased,
which demonstrates the need for it non-local interactions.
