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Photonics

Statistical Analysis of the Photon Loss in Fiber-Optic Communication

Artur Czerwiński, Katarzyna Czerwinska

Published Aug 12, 2022• 15 citations
Publisher

Abstract

In optical communication systems, photons are lost due to the attenuation of the transmission medium. To efficiently implement quantum information protocols, we need to be able to precisely describe such processes. In this paper, we propose statistical methods to estimate the attenuation coefficient of the fiber link. By following the Beer–Lambert law, we utilize the properties of the exponential distribution to estimate the rate parameter based on observable data. In particular, we determine the explicit forms of unbiased estimators that are suitable for censored (truncated) sets of data. Moreover, we focus on minimum-variance methods that ensure a reliable estimation of the attenuation coefficient.

DOI
10.3390/photonics9080568

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In optical communication systems, photons are lost due to the attenuation of the transmission medium. To efficiently implement quantum information protocols, we need to be able to precisely describe such processes. In this paper, we propose statistical methods to estimate the attenuation coefficient of the fiber link. By following the Beer–Lambert law, we utilize the properties of the exponential distribution to estimate the rate parameter based on observable data. In particular, we determine the explicit forms of unbiased estimators that are suitable for censored (truncated) sets of data. Moreover, we focus on minimum-variance methods that ensure a reliable estimation of the attenuation coefficient.
Single-photon sources are used in numerous quantum technologies, from sensing and imaging to communication, making the accurate modeling of their emissions essential. In this work, we propose a statistical framework for describing single-photon emission processes and implement estimators for the exponential distribution to quantify this phenomenon. Our approach provides a reliable method for estimating the radiative decay time, represented by the inverse rate parameter, which is crucial in quantum optics applications. We explore several statistical estimators, including maximum likelihood estimation, minimum-variance unbiased estimator, and best linear unbiased estimator. To validate our theoretical methods, we test the proposed estimators on experimental data, demonstrating their applicability in real-world settings. We also evaluate the performance of these estimators when dealing with censored data, a frequent limitation in photon emission experiments. The analysis allows us to track the performance of the proposed estimators as the amount of available data decreases, providing insights into their reliability for modeling single-photon emission events under limited resources.
The lossy propagation law (generalization of Lambert-Beer's law for classical radiation loss) for non-classical, dual-mode entangled states is derived from first principles, using an infinite-series of beam splitters to model continuous photon loss. This model is general enough to accommodate stray-photon noise along the propagation, as well as amplitude attenuation. An explicit analytical expression for the density matrix as a function of propagation distance is obtained for completely general input states with bounded photon number in each mode. The result is analyzed numerically for various examples of input states. For N00N state input, the loss of coherence and entanglement is super exponential, as predicted by a number of previous studies. However, for generic input states, where the coefficients are generated randomly, the decay of coherence is very different; in fact no worse than the classical Beer-Lambert law. More surprisingly, there is a plateau at a mid-range interval in propagation distance where the loss is in fact sub-classical, following which it resumes the classical rate. The qualitative behavior of the decay of entanglement for two-mode propagation is also analyzed numerically for ensembles of random states using the behavior of negativity as a function of propagation distance.
The analysis of link loss is one of the first and most important steps for the design of an optical communication system. This is particularly vital in quantum communications systems where the information is encoded at the single photon level, and the quantum optical signal cannot be amplified deterministically. In most cases, the desired quantum bit error rate and secure key rate can only be achieved by minimizing the link attenuation and the background noise level in the quantum communication system. In optical fiber implementations, the transmission distance is inherently limited by the loss per unit distance of the optical fiber, meaning fully global coverage is not readily achievable with the current optical fiber backbone networks. To overcome the terrestrial link limitations for quantum communications, long-distance free-space links, using low-Earth orbit satellites are being proposed and implemented. Due to the optical link length, the main contributors to link losses are geometric loss, atmospheric attenuation, and losses associated with pointing and tracking errors. The total link loss is dominated by the geometric loss, therefore, it is important to analyze its importance in relation to the quantum communications link. In this paper, the loss of a low-Earth orbit satellite-to-ground (downlink) quantum communication link is analyzed. The analysis includes losses associate with the channel (geometric and atmospheric) and the receiver system. This paper also compares the data of a known satellite quantum communications mission, highlighting trade-offs in investment for satellite platform and optical ground station. Based on the link loss analysis, decoy state BB84 and E91 protocols were chosen to demonstrate the link performance under an example scenario. The work contributes to the design of the optical ground station for a CubeSat mission.
In this article, we investigate the efficiency of photonic state tomography in the presence of fiber attenuation. The theoretical formalism of the photon loss is provided by implementing methods from the theory of open quantum systems. The quantum state is reconstructed from photon counts obtained for symmetric informationally complete positive operator-valued measures. The number of photons that reach the detectors is numerically modeled by the binomial distribution, which describes the loss of light caused by the medium. This approach allows us to study the quality of state tomography versus the length of the fiber. In particular, we focus on entangled qubits and qutrits, which are sent through fibers of different lengths. The amount of entanglement detected by the measurement scheme is quantified and presented on graphs. The results demonstrate how the quality of photonic tomography depends on the distance between the source and the receiver.
The existing methods of information delivery to the strategic and tactical management of many government agencies are expensive, not always reliable and efficient. Therefore, quantum cryptographic systems (QCS) have been actively developed in recent years. However, there are problems with the use of the QCS associated with the reliability of information transfer. First, the existing fiber-optic communication channels (FOCC) are not designed to transmit single-photon signals, which leads to the complexity of their cryptographic protection. The second is insufficiently methodically developed calculation of energy losses and errors in the evaluation of the characteristics of information transfer in FOCC QCS. In article the analysis of the energy loss factors in the classical fiber-optic channel is carried out and the additive loss formula is discussed in detail. Then we consider the fiber-optic channel of quantum information transmission with the use of integrated optical devices. The additive formula of optical losses in such a channel is discussed. The features of losses in integrated optical devices are shown. The features of quantum cryptographic system of information transmission are considered. As a result, the model of FOCC QCS taking into account energy losses is presented, which allows competently in theoretical terms and visualize the passage of information through modern quantum cryptographically secure telecommunications while providing control in government structures.