  Achieving perfect control over the parameters defining a quantum gate is, in
general, a very challenging task, and at the same time, environmental
interactions can introduce disturbances to the initial states as well. Here we
address the problem of how the imperfections in unitaries and noise present in
the input states affect the entanglement-generating power of a given quantum
gate -- we refer to it as imperfect (noisy) entangling power. We observe that,
when the parameters of a given unitary are chosen randomly from a Gaussian
distribution centered around the desired mean, the quenched average entangling
power -- averaged across multiple random samplings -- exhibits intriguing
behavior like it may increase or show nonmonotonic behavior with the increase
of disorder strength for certain classes of diagonal unitary operators. For
arbitrary unitary operators, the quenched average power tends to stabilize,
showing almost constant behavior with variation in the parameters instead of
oscillating. Our observations also reveal that, in the presence of a local
noise model, the input states that maximize the entangling power of a given
unitary operator differ considerably from the noiseless scenario. Additionally,
we report that the rankings among unitary operators according to their
entangling power in the noiseless case change depending on the noise model and
noise strength.
