  Understanding how a stabilizer circuit responds to different input is
important to formulating an effective strategy for resource management. In this
paper, we further investigate the many ways of using stabilizer operations to
generate a single qubit output from a two-qubit state. In particular, by
restricting the input to certain product states, we discover probabilistic
operations capable of transforming stabilizer circuit outputs back into
stabilizer circuit inputs. These secondary operations are ideally suited for
recovery purposes and require only one extra resource ancilla to succeed. As a
result of reusing qubits in this manner, we present an alternative to the
original state preparation process that can lower the overall costs of
executing any two-qubit stabilizer procedure involving non-stabilizer
resources.
