Exploring the Structural Property of the Optimal Entanglement Policy for Quantum Switch

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 de-coherence 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 shows a threshold-based property between bipartite and tripartite policies under a very general class of weight functions with a weight parameter $\beta$, Empirically, such a threshold-based property also holds for the optimal entanglement policy. In particular, the quantum switch should perform a bipartite or tripartite policy when $\beta$ is below a threshold $\beta_{B}^{*}$ or above a threshold $\beta_{T}^{*}$ ‘, respectively. When $\beta_{B}^{*} < \beta < \beta_{q}^{*}$ “the quantum switch needs to perform a “threshold-based and state-dependent entanglement policy“. We also extend the work to allow a mixture of bipartite and tripartite policies. We theoretically show similar threshold-related relationships between mixed and bipartite/tripartite policies. We carry out extensive numerical experiments to confirm that the optimal entanglement policy has such structural property.