Determination of maximal Gaussian entanglement achievable by feedback-controlled dynamics

We determine a general upper bound for the steady-state entanglement achievable by continuous feedback for systems of any number of bosonic degrees of freedom. We apply such a bound to the specific case of parametric interactions - the most common practical way to generate entanglement in quantum optics - and single out optimal feedback strategies that achieve the maximal entanglement. We also consider the case of feedback schemes entirely restricted to local operations and compare their performance to the optimal, generally nonlocal, schemes.