Noise-enhanced entanglement and squeezing generation by quantum feedback

It is well known that the quantum features of an open system are washed out by the leakage of information into the environment. Having access to the environment one can ask the following question: up to what extent quantum features could be restored by exploiting classical information gathered from environment? In this framework, we study the possibility of enhancing peculiar quantum properties (such as squeezing and entanglement) of bosonic systems subject to quadratic Hamiltonians and a noisy thermal environment, by performing weak Gaussian measurements and conditioned linear driving. We derive general analytical upper bounds for the single mode squeezing and multimode entanglement at steady state, depending only on the Hamiltonian parameters and on the number of thermal excitations of the bath. Our findings show that, rather surprisingly, larger number of thermal excitations in the bath allows for larger steady-state squeezing and entanglement. We provide a rather simple phase-space description, to understand such counter-intuitive result, finding the physical relationship between the bath temperature and the achievable squeezing and entanglement. After that we focus on specific examples and discuss findings of direct applicative interest; in particular we present the details of the optimal feedback strategies achieving the upper bounds, in different relevant physical settings.