The whole from the parts: Markovian stabilizing dynamics and ground-state cooling under locality constraints

We focus on two classes of pure states for a finite-dimensional multipartite quantum system: those that can be identified as unique ground states (UGS) of a locally-constrained Hamiltonian, and those that can be obtained as unique, asymptotically stable equilibria of a Markov quantum dynamics under the same quasi-locality constraints (QLS). While there is an equivalence between (strict) subsets of two classes, namely, states that are UGS of frustration-free Hamiltonians and unique equilibria of purely dissipative dynamics, two paradigmatic entangled states, GHZ and W, offer counterexamples to either implication in the general setting. The intuition that every UGS state can be obtained as the exact steady state of a Markovian cooling process is salvaged only if suitable non-local resources are added. We show that stochastic stabilization of the target UGS state can be achieved if we perform continuous measurement of the global Hamiltonian, while controlling the dynamics with a switching, filtering-based quantum feedback strategy.