The BB84 quantum key distribution using conjugate homodyne detection

Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature values. 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) protocols. 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 suggests that a blind application of the standard security proof could result pessimistic QKD 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 fluctuation cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number statistics 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 new family of QKD protocols, in complementary to the well-established DV-QKD based on single photon detection and CV-QKD based on coherent detection.