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Quantum illumination employs entangled states to detect a weakly reflectivetarget in a thermal bath. The performance of a given entangled state isevaluated from the minimum error probability in the asymptotic limit, which iscompared against the optimal coherent state scheme. We derive an upper bound aswell as a lower bound on the asymptotic minimum error probability, as functionsof the quantum Fisher information. The upper bound can be achieved using arepetitive local strategy. This allows us to compare the optimal performance ofdefinite-photon-number entangled states against that of the coherent statesunder local strategies. When optimized under the constraint of a fixed totalenergy, we find that a coherent state outperforms the definite-photon-numberentangled state with the same signal energy.

Quantum illumination with non-Gaussian states: Bounds on the minimum error probability using quantum Fisher information