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arXiv:2511.10755

Optimal propagation distance for maximal biphoton entanglement through the weakly turbulent atmosphere

Luchang Niu, Saleem Iqbal, Yang Xu, Robert W. Boyd

quant-phSubmitted Nov 13, 2025• Announced Nov 17, 2025• 0 citations
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Abstract

Understanding the influence of atmospheric turbulence on the propagation of entangled biphoton states is essential for free-space quantum communication protocols. Using the extended Huygens-Fresnel principle and the Kolmogorov turbulence model, we derive an analytical expression for the combined density operator of the signal and idler fields generated via SPDC, following propagation through separate turbulent channels. By expressing this density operator in the continuous position basis, we show how the spatial correlations between signal and idler persist through turbulence despite the loss of state purity, as they transition from being quantum to classical in nature. We further identify a finite range of propagation distances over which the angle-OAM entanglement is maximized, which provides valuable insights for designing free-space quantum communication links operating over several kilometers through the turbulent atmosphere.

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Photonics for Quantum (PfQ)•Jun 14, 2024•2 citations
Understanding the influence of atmospheric turbulence on the propagation of entangled biphoton states is essential for free-space quantum communication protocols. Using the extended Huygens-Fresnel principle and the Kolmogorov turbulence model, we derive an analytical expression for the combined density operator of the signal and idler fields generated via SPDC, following propagation through separate turbulent channels. By expressing this density operator in the continuous position basis, we show how the spatial correlations between signal and idler persist through turbulence despite the loss of state purity, as they transition from being quantum to classical in nature. We further identify a finite range of propagation distances over which the angle-OAM entanglement is maximized, which provides valuable insights for designing free-space quantum communication links operating over several kilometers through the turbulent atmosphere.
In this paper, we investigate the propagation of two-mode spatially Gaussian-entangled quantum light fields passing through the turbulence atmosphere. From the propagation formula of the two-mode wave function in the position representation, we have derived the analytical expressions for the fidelity, purity and logarithmic negativity (entanglement) of the resulting quantum state after the long-distance atmospheric transportation. Based on the derived formulae, the effects of the atmospheric turbulences on the evolutions of quantum properties of the resulting two-mode quantum state are discussed in detail under different input parameters of the initial two-mode quantum state. The results show that the maximal distributing distance of quantum entanglement is strongly dependent on the atmospheric conditions: when the atmospheric turbulence becomes stronger and stronger, the maximal distance becomes shorter and shorter, and both the fidelity and purity decrease quicker and quicker as functions of propagating distances. Under a certain atmospheric condition, with the increasing of the input entanglement of the initial two-mode spatially Gaussian-entangled quantum state, the maximal distributing distance for preserving the entanglement gradually increases and always has a saturated (upper) limitation, and both the evolutions of the fidelity and purity are affected by the input parameters of the initial two-mode quantum state, Finally the optimal parameters of the input two-mode quantum state with the fixed input entanglement are discussed in order to obtain the optimal transfer distribution of the quantum entanglement over a long distance under a certain atmosphere. Our theoretical results are very helpful for building the distribution of the quantum entanglement via free-space atmosphere link.
The orbital angular momentum (OAM) state of light can potentially be used to implement higher dimensional entangled systems for quantum communication. Unfortunately, optical fibers in use today support only modes with zero OAM values. Free-space quantum communication is an alternative to traditional way of communicating through optical fibers. However the refractive index fluctuation of the atmosphere gives rise to random phase aberrations on a propagating optical beam. To transmit quantum information successfully through a free-space optical channel, one needs to understand how atmospheric turbulence influences quantum entanglement. Here, we present a numerical study of the evolution of quantum entanglement between a pair of qubits. The qubits consist of photons entangled in the OAM basis. The photons propagate in a turbulent atmosphere modeled by a series of consecutive phase screens based on the Kolmogorov theory of turbulence. Maximally entangled initial states are considered, and the concurrence is used as a measure of entanglement. We show how the evolution of entanglement is influenced by various parameters such as the beam waist, the strength of the turbulence and the wavelength of the beam. We restricted our analysis to the OAM values l = ±1 and we compared our results to previous work.
Orbital angular momentum (OAM) entangled bi-photons are a resource for the higher dimensional implementation of quantum cryptography, which allows secure communication over various channels. In the case where free-space is used as communication channel the initial OAM entangled bi-photon loses some or even all of its entanglement because of the scintillation that it experiences while propagating through the turbulence in the atmosphere. This decoherence of OAM entanglement has so far only been studied for the case of weak turbulence. Unfortunately, it is the more challenging strong turbulence scenario that is relevant for the practical implementation of free-space quantum communication through the atmosphere. Using an approach that differs from previous approaches, we derive a master equation for the evolution of an OAM entangled bi-photon during propagation through turbulence. However, in our approach the equation contains a derivative with respect to the propagation distance instead of time. The principle is to consider the propagation over an infinitesimal distance of OAM basis states through a random medium. This approach allows one to include, not only the effect of turbulence of arbitrary strength, but also the effect of the inner and outer scale of the turbulence, as represented by the Tartarskii and von Karman spectra. The resulting expression can predict the rates of decoherence for arbitrary initial OAM entangled states and can be used to calculate the concurrence, which measures the amount of entanglement, as a function of propagation distance for different initial entangled OAM states.
We extend the theory of detection probabilities of single-photon communication in turbulent atmosphere to the entangled case and derive analytical expressions for detection probabilities. We show that the rotational field correlation in the entangled case cannot be expressed as a straightforward extension from the disentangled case. By considering the orbital angular momentum (OAM) entangled Laguerre-Gaussian (LG) beams for illustration, we explore the effect of non-Kolmogorov atmospheric turbulence on the probabilities of both the biphoton detection and the single-photon detection. The entanglement of OAM LG beams contributes positively to the faithful detection probability. The change of maximal crosstalk probability in the detection process is also explored, which displays the non-linear dependence on the crosstalk quantum number.
Quantum entanglement is critical to build the backbone of all quantum technologies. Quantum networks, quantum computations, and quantum communication networking is based on long-range distribution of entangled photons and teleportation of photon qubit states. In order to understand quantum entanglement, characterization of atmospheric turbulence and its effects on propagating quantum states in free-space is essential. One method of photon entanglement is using a photon’s polarization. In this paper, we report results using polarization entangled signal and idler photons. The results may be applicable to support various quantum computing, encryption, and other qubit based high-performance communication protocols. Classically, the degradation of beam quality occurs due to many factors but primarily due to the distortion of spatial and temporal fields of refractive index. However, behavior of single photons through similar turbulent media creates a different set of challenges pointing to integrity of quantum states during propagation. We study this behavior by analyzing quantum states and the degree of entanglement in real-time and correlating it to known atmospheric models, (refractive index structure parameter), and relevant propagation path parameters. This experimental study was performed initially in a controlled laboratory environment, and then devised to be implemented outdoors over a 100-meter free space communication link.
Quantum entanglement is an essential element for building the backbone of quantum information systems. Our particular interest lies in long-range distribution of entangled photons to facilitate secure data transfer in free space. To achieve this, we rely on photon pairs generated in such a way that their polarization characteristics represent the corresponding qubit states and have a high degree of correlation in measurements. The main focus of this paper is integrity of the quantum states in free-space channels. When transmitted in atmosphere, classical signals suffer from wave front distortions caused by the spatial and temporal fields of the refractive index. However, this mechanism does not have the same bearing on qubit values and their correlation. We study the effects of turbulence on quantum states by utilizing a laboratory testbed that includes an atmospheric chamber developed by the AFRL. It uses a system of controlled components capable of creating various turbulence conditions. When polarized signals are passed through the atmospheric chamber, we analyze the corresponding quantum states and evaluate the degree of entanglement using our mathematical models and existing metrics.