Stabilizing Entangled States with Quasi-Local Quantum Dynamical Semigroups

TL;DR

This paper presents a method to determine if a pure entangled state can be asymptotically stabilized using local dissipative quantum dynamics, offering an explicit test and connections to Hamiltonian formalism.

Contribution

It introduces an explicit stabilization test for pure states under locality constraints, extending existing results and linking to frustration-free Hamiltonians.

Findings

Provided a criterion for state stabilization under local dissipative dynamics

Connected stabilization conditions to frustration-free parent Hamiltonians

Discussed control implementation via switching output-feedback law

Abstract

We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Beside recovering existing results for a large class of physically relevant entangled states, our approach has the advantage of providing an explicit stabilization test solely based on the input state and constraints of the problem. Connections with the formalism of frustration-free parent Hamiltonians are discussed, as well as control implementations in terms of a switching output-feedback law.