  This paper solves the open problem of characterizing the performance of
quantum illumination (QI) with discrete variable states. By devising a novel
quantum measurement approach along with meticulous analysis, our investigation
demonstrates that, in the limit as $M \rightarrow \infty$, the maximally
entangled $M$ mode Bell state achieves optimal performance, matching the
two-mode squeezed vacuum in a high-noise regime and exceeding it in low-noise.
This result challenges the dominance of continuous variable states in photonic
sensing applications and extends the novelty of QI to regimes where no quantum
advantage was believed to exist. A closer analysis reveals that this advantage
stems from retained entanglement in the transmitted Bell state, a
paradigm-shifting discovery since interaction with the environment in optical
systems is believed to break entanglement. The complete mathematical analysis
of this work provides granular insights into the interaction between photonic
systems and environmental noise, motivating further research into discrete
variable quantum sensing.
