Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature. In this paper we explore the possibility of operating a conjugate homodyne detection system in “photon counting” mode to implement discrete-variable (DV) quantum key distribution (QKD). A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures $X$ and $P$ of the incoming quantum state. In classical electrodynamics, $X^2+P^2$ is proportional to the energy (the photon number) of the input light. In quantum optics, $X$ and $P$ do not commute and thus the above photon-number measurement is intrinsically noisy. This implies that a blind application of standard security proofs of QKD could result in pessimistic performance. We overcome this obstacle by taking advantage of two special features of the proposed detection scheme. First, the fundamental detection noise associated with vacuum fluctuations cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number distribution at the receiver's end can place additional constraints on possible attacks from the adversary. As an example, we study the security of the BB84 QKD using conjugate homodyne detection and evaluate its performance through numerical simulations. This study may open the door to a family of QKD protocols, complementary to the well-established DV-QKD based on single-photon detection and CV-QKD based on coherent detection.

中文翻译：

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Bennett-Brassard 1984使用共轭零差检测的量子密钥分布

光学零差检测已广泛用于连续变量（CV）量子信息处理中以测量场正交。在本文中，我们探索了在“光子计数”模式下操作共轭零差检测系统以实现离散变量（DV）量子密钥分配（QKD）的可能性。共轭零差检测系统由分束器和两个光学零差检测器组成，可同时测量一对共轭正交$X$ 和 $P$进入的量子态 在经典的电动力学中，$X^2+P^2$与输入光的能量（光子数）成正比。在量子光学中$X$ 和 $P$不要通勤，因此上述光子数测量本质上是有噪声的。这意味着盲目使用QKD的标准安全性证明可能会导致悲观的性能。我们利用建议的检测方案的两个特殊功能克服了这一障碍。首先，与真空波动相关的基本检测噪声无法由外部对手操纵。其次，在接收器端重建光子数量分布的能力可能会对来自对手的可能攻击施加其他限制。例如，我们使用共轭零差检测技术研究BB84 QKD的安全性，并通过数值模拟评估其性能。这项研究可能会打开一系列QKD协议的大门，