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Physica Scripta

Channel capacity and quantum entanglement of autofocusing hypergeometric-Gaussian beams through non-Kolmogorov turbulence

Xiangjiang Bao, Yun Zhu, Jicheng Wang, Zheng-Da Hu

Published Jan 15, 2023• 9 citations
Publisher

Abstract

Abstract We establish propagation models for distributing autofocusing hypergeometric-Gaussian (HyGG) beams via non-Kolmogorov atmospheric turbulence in the single-photon and biphoton cases. Analytical expressions of the channel capacity and entanglement are employed to explore the communication performance in turbulence. It can be demonstrated that in the single-photon case, a lower hollowness parameter and larger topological charge could contribute to the anti-interference ability of HyGG beams. Such an anti-interference ability could be affected by the autofocusing distance more severely for beams with larger topological charges. In addition, the channel capacity of beams at a certain distance decays rapidly at first before it grows steadily with the increase in the power-law exponent of the non-Kolmogorov spectrum. For the biphoton case, the higher hollowness parameter, larger power-law exponent of the non-Kolmogorov spectrum and larger topological charge make HyGG beams maintain a high concurrence at longer distances. We believe that our results could serve as a reference for improving the quality of orbital-angular-momentum communication of HyGG beams via atmospheric turbulence.

DOI
10.1088/1402-4896/acb328

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Abstract We establish propagation models for distributing autofocusing hypergeometric-Gaussian (HyGG) beams via non-Kolmogorov atmospheric turbulence in the single-photon and biphoton cases. Analytical expressions of the channel capacity and entanglement are employed to explore the communication performance in turbulence. It can be demonstrated that in the single-photon case, a lower hollowness parameter and larger topological charge could contribute to the anti-interference ability of HyGG beams. Such an anti-interference ability could be affected by the autofocusing distance more severely for beams with larger topological charges. In addition, the channel capacity of beams at a certain distance decays rapidly at first before it grows steadily with the increase in the power-law exponent of the non-Kolmogorov spectrum. For the biphoton case, the higher hollowness parameter, larger power-law exponent of the non-Kolmogorov spectrum and larger topological charge make HyGG beams maintain a high concurrence at longer distances. We believe that our results could serve as a reference for improving the quality of orbital-angular-momentum communication of HyGG beams via atmospheric turbulence.
Abstract We use Hypergeometric Gaussian-II (HyGG-II) modes to investigate the impacts of non-Kolmogorov atmospheric turbulence on the Holevo channel capacity of a quantum communication scheme. The capacity of HyGG-II modes can be higher than that of Laguerre–Gaussian modes via modulating the hollowness parameter. The influences of low-order turbulence aberrations including tilt, defocus, astigmatism, and coma on the capacity are also explored. Generally, tilt aberration dominates among all low-order aberrations and defocus and astigmatism aberrations are always negligible. By contrast, the effect of coma aberration can be enhanced to be non-negligible when the turbulence strength or the channel zenith angle is enhanced. We also show that only the total and tilt aberrations are sensitive to the non-Kolmogorov power-law exponent. Our results may contribute to the quantum optical communication as well as aberration compensation in turbulent channels utilizing the novel family of vortex beams.
The propagation properties of Laguerre-Gaussian beams in oceanic turbulence are investigated for both single-photon and biphoton cases. For single-photon communication, the channel capacity and trace distance are employed, both of which effectively reveal the communication performance via different viewpoints. For the biphoton case, we consider distributions of quantum resources including entanglement and quantum coherence. Turbulence conditions with a larger inner-scale and anisotropic factors, higher dissipation rate of kinetic energy, lower dissipation rate of the mean-squared temperature, and lower temperature-salinity contribution ratio combined with longer wavelength and an appropriate range of optimal beam width are beneficial to communication performances. Our results provide theoretical significance to improve the orbital-angular-momentum communication via oceanic turbulence.
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.
We consider the non-horizontal distributions of orbital angular momentum biphotons through free-space atmospheric channels, in which case the non-Kolmogorov turbulent effects shall be considered. By considering the case of initial non-perfect resource, i.e., the orbital angular momentum biphotons are initially prepared in an extended Werner-like state, we investigate the non-Kolmogorov effects on the propagations of nonclassical correlations, including quantum entanglement and quantum discord. It is found that universal decay laws of entanglement and discord also exist for non-Kolmogorov turbulence but with their decay curves different from that of entanglement for Kolmogorov turbulence reported by Leonhard et al. [Phys. Rev. A91, 012345 (2015)PLRAAN1050-294710.1103/PhysRevA.91.012345]. We show that the universal decay laws are dependent on the power-law exponent of the non-Kolmogorov spectrum and compare the differences of decay properties between entanglement and discord caused by non-Kolmogorov turbulence.
Two photonic qubits, initially maximally entangled in OAM modes of Hermite-Gaussian HG vortex beam, propagating through non-Kolmogorov turbulence are investigated numerically. The influences of turbulence parameter (i.e., the generalized exponent, the outer scale of turbulence, and the inner scale of turbulence) and OAM values on the entanglement evolution of two photon are investigated and compared with those of the Laguerre-Gaussian (LG) beam. The results indicate that the OAM entanglement to be more robust in turbulence for the higher OAM values, the higher generalized exponent. Moreover, the influence of the turbulence inner scale and outer scale on OAM entanglement can be ignored. The OAM entanglement of HG vortex beam is better than the OAM entanglement of LG beam for resisting the entanglement decoherence of atmosphere turbulence under the same conditions.
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.