Steady-State Entanglement by Engineered Quasi-Local Markovian Dissipation

TL;DR

This paper develops methods to engineer Markovian dissipation processes that stabilize specific entangled states in multipartite quantum systems, considering physical locality constraints and control options.

Contribution

It introduces algorithms for constructing Markovian dynamics to stabilize target entangled states, extending the set of stabilizable states under locality constraints.

Findings

Quasi-local control protocols for GHZ and W states on n qubits.

No scalable stabilization from arbitrary states for GHZ states.

Scalable stabilization of W states with specific initial conditions.

Abstract

We characterize and construct time-independent Markovian dynamics that drive a finite-dimensional multipartite quantum system into a target (pure) entangled steady state, subject to physical locality constraints. In situations where the desired stabilization task can not be attained solely based on local dissipative means, we allow for local Hamiltonian control or, if the latter is not an option, we suitably restrict the set of admissible initial states. In both cases, we provide algorithms for constructing a master equation that achieves the intended objective and show how this can genuinely extend the manifold of stabilizable states. In particular, we present quasi-local control protocols for dissipatively engineering multipartite GHZ "cat" states and W states on $n$ qubits. For GHZ states, we find that no scalable procedure exists for achieving stabilization from arbitrary initial states, whereas this is possible for a target W state by a suitable combination of a two-body Hamiltonian and dissipators. Interestingly, for both entanglement classes, we show that quasi-local stabilization may be scalably achieved conditional to initialization of the system in a large, appropriately chosen subspace.