State Engineering of Unsteerable Hamiltonians

Lindbladian dynamics of open systems may be employed to steer a many-body system towards a non-trivial ground state of a local Hamiltonian. Such protocols provide us with tunable platforms facilitating the engineering and study of non-trivial many-body states. Steering towards a degenerate ground state manifold provides us with a protected platform to employ many-body states as a resource for quantum information processing. Notably, ground states of frustrated local Hamiltonians have been known not to be amenable to steering protocols. Revisiting this intricate physics we report two new results: (i) we find a broad class of (geometrically) frustrated local Hamiltonians for which steering of the ground state manifold is possible through a sequence of discrete steering steps. Following the steering dynamics, states within the degenerate ground-state manifold keep evolving in a non-stationary manner. (ii) For the class of Hamiltonians with ground states which are non-steerable through local superoperators, we derive a "glass floor" on how close to the ground state one can get implementing a steering protocol. This is expressed invoking the concept of cooling-by-steering (a lower bound of the achievable temperature), or through an upper bound of the achievable fidelity. Our work provides a systematic outline for studying quantum state manipulation of a broad class of strongly correlated states.