用对角数信号态鉴别量子光学分束器通道：在量子读取和目标探测中的应用
Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection
摘要：
本文考虑了利用纠缠在M个信号模和M'个闲频模对上的一般量子探测态，以最小的误差概率区分两个复值反射率不等的光学分束器通道的问题。我们得到了一个下界的输出状态保真度有效的任何纯输入状态。我们定义了数对角信号（NDS）状态作为输入状态，其信号模式中的密度算子在多模数基中是对角的。对于这样的输入状态，我们推导出一系列公式的最佳错误概率，输出状态的保真度，和的错误概率上界的Boffoff型。对于经典数字存储器的量子读出和目标探测（反射率为实值）的特殊情况，我们证明了对于给定的输入信号光子概率分布，保真度由具有该分布的NDS态最小化;对于给定的平均总信号能量Ns，保真度由具有Ns个总信号光子的多模Fock态最小化。对于一个理想的存储器的读取，它示出，福克状态输入最小化的Beskoff界。对于高损耗条件下的目标检测，一个不去的结果表明缺乏明显的量子优势相干态发射机推导。比较了不同反射率下，数态和双模压缩真空态（或EPR态）发射机相对于相干态发射机的量子读出误差概率性能.虽然非经典状态一般比相干状态表现得更好，但定量性能增益取决于反射率的值而不同。
英文摘要：
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. For the special cases of quantum reading of a classical digital memory and target detection (for which the reflectivities are real valued), we show that for a given input signal photon probability distribution, the fidelity is minimized by the NDS states with 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 signal photons. For reading of an ideal memory, it is shown that Fock state inputs minimize the Chernoff bound. For target detection under high-loss conditions, a no-go result showing the lack of appreciable quantum advantage over coherent state transmitters is derived. A comparison of the error probability performance for quantum reading of number state and two-mode squeezed vacuum state (or EPR state) transmitters relative to coherent state transmitters is presented for various values of the reflectances. While the nonclassical states in general perform better than the coherent state, the quantitative performance gains differ depending on the values of the reflectances.
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