Abstract Rigorous study of optical communication processes has become interesting since around 1970. Especially, quantum information theory has been developed in both mathematics and engineering. In this paper, by controlling the energy associated with a quantum input state, we obtain an optimal solution (optimal state, optical modulation, etc.) giving the minimum value to the error probability in the attenuation optical communication process. For instance, we find some relations between the energy constraint of the input state and the optimal error probabilities in each modulation.
This paper presents a practical optical communication framework that transmits binary information using distinct coherent states characterized by different mean photon numbers and detects the received signals via threshold-based photon counting. Unlike conventional approaches that often assume idealized detection environments, we rigorously analyze the performance of the proposed scheme under three realistic scenarios: (i) noise-free channels, (ii) channels impaired by additive Poisson noise, and (iii) turbulent free-space optical channels with fading and background noise. The coherent-state modulation enables energy-efficient transmission in the quantum-limited regime while the photon-counting receiver employs a statistically optimized decision threshold to discriminate between received photon-count levels. To address the lack of instantaneous channel state information in fading environments, we further propose a pilot-based channel estimation method that enables adaptive threshold selection. Closed-form expressions for decision thresholds and error probabilities are derived, and the effectiveness of the scheme is validated through detailed numerical simulations. These results offer design insights for photon-efficient, low-power optical communication systems operating under realistic physical impairments.
This paper investigates the performance of coherent-state quantum optical wireless communication systems operating over atmospheric turbulence channels with pointing errors (PEs). The average error probability (AEP) and average achievable rate (AAR) are analyzed for on–off keying (OOK) and binary phase-shift keying (BPSK) signaling under photon-counting (PC), homodyne, and optimal Helstrom detection. The proposed framework jointly incorporates deterministic path loss, atmospheric turbulence, and PEs, and accommodates multiple statistical channel models, including Gamma-Gamma (GG), doubly inverted Gamma-Gamma (IGGG), and Fisher-Snedecor
F distributions, within a unified analytical formulation. Closed-form expressions for AEP and AAR are derived via direct probability density function (PDF)-based integration of the conditional error probability, along with high-photon-number asymptotic approximations that provide insight into performance scaling behavior. Numerical results validate the analytical expressions and demonstrate the impact of PEs on system performance. The analysis further enables systematic comparison between classical and optimal quantum detection schemes and quantifies the achievable performance gains under different channel conditions. These results provide useful design insights for modulation and receiver selection in turbulent free-space optical (FSO) communication systems.