Structural Property of the Optimal Entanglement Policy for Quantum Network Switch: An MDP Approach

A quantum switch is one of the most fundamental network elements for connecting different quantum devices. In this paper, we explore the “optimal entanglement policy” of a quantum switch under a scenario where the stored and entangled qubits in the quantum switch may undergo a decoherence process. Finding an optimal entanglement policy is important as it enables a quantum switch to make a judicious basis measurement based on the number of existing link-level entanglements to maximize the “weighted throughput”. We use a Markov decision process framework to model the dynamics of the quantum switch, and theoretically reveal a threshold-based relationship between bipartite and tripartite policies under a very general class of weight functions with a weight parameter β. We further extend our analysis to uncover athreshold-based structure of optimal policies. In particular, the optimal policy for the quantum switch is a bipartite or tripartite policy when β is below a threshold β∗Bor above a threshold β∗T, respectively. When β∗B∗T, the optimal policy becomes a “threshold-based and state-dependent entanglement policy”. We also extend the work to allow a mixture of bipartite and tripartite policies by introducing a state-dependent mixed action. We theoretically show threshold-related relationships between mixed and bipartite/tripartite policies. Moreover, we extend this analysis to study optimal policies and characterize the threshold-based structure when the mixed action is considered. We carry out extensive numerical experiments to confirm that the optimal entanglement policy has such structural property when the mixed action is considered or not.