The performance of free-space optical quantum communications deteriorates due to the presence of atmosphere turbulence. In this paper, the P-function of a coherent state passing through a turbulent atmosphere channel in the presence of thermal noise is derived using the additive property of the thermal noise channel. The analytical form of the density operator for this turbulent coherent state and its corresponding matrix representation in Fock basis is deducted. Using this matrix representation of density operator for turbulent coherent state, the error probability of optical quantum communication system for binary phase shift keying is analyzed.
The performance of free-space optical quantum communications deteriorates due to the presence of atmosphere turbulence. In this paper, the P-function of a coherent state passing through a turbulent atmosphere channel in the presence of thermal noise is derived using the additive property of the thermal noise channel. The analytical form of the density operator for this turbulent coherent state and its corresponding matrix representation in Fock basis is deducted. Using this matrix representation of density operator for turbulent coherent state, the error probability of optical quantum communication system for binary phase shift keying is analyzed.
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.
An optical quantum communication system with receiver diversity is proposed for free-space communication using the optical combining technique and a generalized Kennedy receiver. The quantum channel model of the proposed system is established using the P -representation in the presence of both turbulence and thermal noise. A conditional dynamics based Kennedy receiver with threshold detection is proposed to mitigate the influence of both turbulence and thermal noise. The error probabilities for different types of generalized Kennedy receiver, i.e., the Kennedy receiver, the Type-II receiver, and the conditional dynamics based Kennedy receiver, are analytically studied and the lower bounds for these error probabilities are obtained. Numerical results show that both the Kennedy receiver and the Type-II receiver fail in the presence of either turbulence or thermal noise. The performance of the proposed conditional dynamics based Kennedy receiver with threshold detection can surpass the standard quantum limit given by the homodyne receiver in either weak turbulence or small thermal noise.
We study the channel capacity for orbital angular momentum (OAM) based quantum free-space optical communications. Inspired by recent demonstrations for OAM-based single-photon communication, we construct the quantum density operator in matrix form, based on OAM eigenkets, and determine the quantum channel model suitable for study of the quantum communication over atmospheric turbulence channels. The quantum channel model is derived from OAM eigenkets transition probabilities. By using this model we determine the OAM quantum channel capacity in the presence of atmospheric turbulence. The proposed quantum channel model is of high importance for future study of quantum error correction coding to extend the transmission distance and data rate of free-space quantum communications.
In this letter, we analyze the average probability of error of quantum modulation schemes in weakly turbulent quantum communication channels utilizing coherent states. Atmospheric turbulence-induced fading is a significant challenge that degrades the performance of free-space quantum communication systems. We derive and present closed-form expressions for the average probability of error for various detection methods: classical (shot-noise limited) single-photon detection, coherent detection, and the optimal quantum hypothesis-testing (Helstrom) detection for binary quantum modulation schemes. Our analysis focuses on the transmission of classical data modulated by quantum coherent states over a log-normal turbulent channel. Additionally, we discuss the lower bounds of the average capacities for Helstrom detection, providing comprehensive insights into the achievable information rates in realistic atmospheric conditions. The derived expressions show excellent agreement with numerical Monte Carlo simulations across a broad range of average transmitted photon numbers, offering valuable guidelines for the design and optimization of quantum communication systems.
This work analyzes a terrestrial-based free-space quantum key distribution system employing quadrature-phase shift keying signaling (QKD-QPSK). An analytical framework is proposed to determine various joint probabilities under the gamma-gamma turbulence channel model without utilizing the Gaussian–Laguerre (GL) method. Although GL-based method provides ease of computation of integral forms, but it is not always stable. Using derived joint probabilities, novel analytical expressions for the probability of sifted keys (Psift), quantum bit error rate (QBER), error probability for the eavesdropper (Peve), and the ergodic secret-key rate (ESKR) are determined for QKD-QPSK system. This work also reveals that the QKD-QPSK system can be transformed into QKD-based binary phase-shift keying (QKD-BPSK) system. Furthermore, using the proposed analytical framework, all the considered performance metrics are also evaluated for the QKD-BPSK system. Finally, QKD-QPSK and QKD-BPSK systems are compared under moderate and strong turbulence regimes. Comparative results indicate that QKD-QPSK outperforms QKD-BPSK in terms of Peve. However, QKD-BPSK is superior to QKD-QPSK for Psiftand QBER. Furthermore, a positive ESKR can be achieved for both systems with the proper selection of threshold coefficient (ρ) and transmitted power (Pt).
In previous research on quantum information the- ory, channel capacity of the lossy bosonic channel that is a model of free space or an ideal optical fiber was shown. However, in the optical space communication, the influence of temporal and spatial change in the propagation path on the quantum communication has not been clarified. In order to clarify them, we have studied properties of quantum communications via channels with various fluctuations. We consider phase noise since phase fluctuates by a slight drift of the receiver and it has not been considered well compared to amplitude fluctuation. In this paper, we compute the error probability of the optimum quantum receiver in the presence of phase noise and compare with that of homodyne receiver when BPSK coherent-state signals are used. Then we consider the robustness of the optimum receiver against phase fluctuations. I. INTRODUCTION In order to increase the communication rate, higher fre- quency signals should be used. Light wave has a very high frequency in particular, optical communication systems using this were realized by the invention of the laser. Currently, optical fiber communication systems which consist of laser light source, optical fiber, and photodetector have come to be generally used. Moreover, light is also a promising carrier for wireless or space communications with high capacity. However, the performance of communication systems of this scheme has been approached to the theoretical limit. The factor is due to quantum mechanical effects of light, called quantum noise. Quantum noise increases in proportion to the frequency of the electromagnetic wave. Therefore, it cannot be ignored in the high frequency band, such as optical frequency. In addition, quantum noise is essentially different from the classical noise such as thermal noise. Therefore, it is not possible to suppress quantum noise using information theory which is the basis of current communication technology. That is, in order to realize higher communication rate, a theory which can describe accurately the quantum mechanical nature of light is required. For this reason, we should study quantum information theory which had been introduced axioms of quantum mechanics into the conventional information theory (2), (3), (4). As a previous study, the channel capacity of the lossy bosonic channel which is a model of free space and optical fiber communications was shown (5). That is, performance of ideal quantum communication was clarified. Therefore, as the next step, a study aiming at the actual use is required. As an example, the study on communication model that takes account of the propagation path environment will be needed. In classical communication, such models have been studied as a theory for realizing mobile communications, etc. However, in quantum communication, there are few such results of study now. This study is intended to clarify the influence of temporal and spatial change of the propagation path environment for the quantum communication. We consider phase noise since phase fluctuates by a slight drift of the receiver and it has not been considered well compared to amplitude fluctuation.