  In the standard von Neumann interaction used in Quantum measurements, the
chosen observable to which the environment (apparatus) entangles is exactly
reproduced in the state of the environment, thereby decohering the quantum
system in the eigenbasis of the observable. We relax this by allowing for
imperfect measurements whereby the environment evolves to a state that
approximately, but not exactly, reflects the state of the system. In this
scheme it is possible to attain approximate decoherence of conjugate quantities
that resembles classical physics, which we demonstrate using an example.
