On the Stochastic Analysis of aQuantum Entanglement Switch

ABSTRACT We study a quantum entanglement switch that serves k users in a star topology.Wemodel variants of the system usingMarkov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. While it is more accurate to use a discrete-time Markov chain (DTMC) tomodel such systems, we quickly encounter practical constraints of using this technique and switch to using continuous-time Markov chains (CTMCs). Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can model the effects of decoherence of quantum states fairly easily using CTMCs. We also compare the results we obtain from the DTMC against the CTMC in the case of homogeneous links and infinite buffer, and learn that the CTMC is a reasonable approximation of the DTMC. From numerical observations, we discover that buffer size has little effect on capacity and expected number of stored qubits. We also learn that while decoherence does not significantly affect these performance metrics in homogeneous systems, it can have drastic consequences when heterogeneity is introduced.