Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection

Understand

We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly.

• We obtain a lower bound on the output state fidelity valid for any pure input state.
• We define number-diagonal signal (NDS) states to be input states whose density operator in the signal modes is diagonal in the multimode number basis.
• For such input states, we derive series formulas for the optimal error probability, the output state fidelity, and the Chernoff-type upper bounds on the error probability.