Quantum sensor network with probabilistic entanglment generation

One of the most promising applications of quantum networks is entanglement assisted sensing, i.e., exploiting quantum correlations to improve the precision bound for applications such as precision timekeeping, long-baseline imaging, magnetic-field sensing, and biological imaging. When measuring multiple spatially distributed parameters, current literature focuses on entanglement among qubits in the discrete variable case, and entangled squeezing modes in the continuous variable case. However, it can be difficult to ensure all sensors pre-share entanglement of high-enough fidelity. Our work probes the space between fully entangled and fully classical sensor networks by modeling a star-topology network with probabilistic entanglement generation that is attempting to estimate a generalized parameter. The quantum Fisher Information is used to determine which protocols best utilize entanglement as a resource for different network conditions. It is shown that without entanglement distillation there is a threshold fidelity below which classical sensing is preferable. For a network with a given number of sensors and links characterized by initial link fidelities and probabilities of success, this work outlines when to use entanglement, when to store it, and when it needs to be distilled.