Subspace controllability of multi-partite spin networks

TL;DR

This paper characterizes when multipartite spin networks can be fully controlled within their invariant subspaces, using graph theory to unify previous results in quantum control.

Contribution

It provides an exact graph-theoretic characterization of subspace controllability in multipartite spin networks, extending and unifying prior work.

Findings

Graph-theoretic conditions for controllability are established.

Subspace controllability depends on the network's symmetry and interaction structure.

The results unify previous controllability criteria for quantum spin systems.

Abstract

In a network of spin 1/2 particles, controlled through an external electro-magnetic field, the gyromagnetic ratio of each spin is a parameter that characterizes the interaction of the spin with the external control field. Multipartite networks are such that the spins are divided into subsets according to their gyromagnetic ratio and spins in one set interact in the same way with all spins in another set. Due to the presence of symmetries in this type of systems, the underlying Hilbert state space splits into invariant subspaces for the dynamics. Subspace controllability is verified if every unitary evolution can be generated by the dynamics on these subspaces. We give an exact characterization, in term of graph theoretic conditions, of subspace controllability for multipartite quantum spin networks. This extends and unifies previous results.