  It is known that one can do quantum error correction without syndrome
measurement, which is often done in operator quantum error correction (OQEC).
However, the physical realization could be challenging, especially when the
recovery process involves high-rank projection operators and a superoperator.
We use operator theory to improve OQEC so that the implementation can always be
done by unitary gates followed by a partial trace operation. Examples are given
to show that our error correction scheme outperforms the existing ones in
various scenarios.
