In this talk, I will talk about our recent results in quantum illumination with photon number entangled states. I will first give an
introduction to quantum hypothesis testing and then on quantum illumination. Then I will present our recent result on possibilities of using photon number entangled states. When optimized under the constraint of a fixed total energy, we find that a coherent state utperforms the definite photon-number entangled states with the same signal energy.
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