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We consider the problem of distinguishing, with minimum probability of error,two optical beam-splitter channels with unequal complex-valued reflectivitiesusing general quantum probe states entangled over M signal and M' idler modepairs of which the signal modes are bounced off the beam splitter while theidler modes are retained losslessly. We obtain a lower bound on the outputstate 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 isdiagonal in the multimode number basis. For such input states, we derive seriesformulas for the optimal error probability, the output state fidelity, and theChernoff-type upper bounds on the error probability. For the special cases ofquantum reading of a classical digital memory and target detection (for whichthe reflectivities are real valued), we show that for a given input signalphoton probability distribution, the fidelity is minimized by the NDS stateswith that distribution and that for a given average total signal energy N_s,the fidelity is minimized by any multimode Fock state with N_s total signalphotons. For reading of an ideal memory, it is shown that Fock state inputsminimize the Chernoff bound. For target detection under high-loss conditions, ano-go result showing the lack of appreciable quantum advantage over coherentstate transmitters is derived. A comparison of the error probabilityperformance for quantum reading of number state and two-mode squeezed vacuumstate (or EPR state) transmitters relative to coherent state transmitters ispresented for various values of the reflectances. While the nonclassical statesin general perform better than the coherent state, the quantitative performancegains differ depending on the values of the reflectances.

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