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Optics Express

Quantum coherence of thermal biphoton orbital angular momentum state and its distribution in non-Kolmogorov atmospheric turbulence

Zheng-Da Hu, Yun Zhu, Jicheng Wang

Published May 16, 2022• 3 citations
Publisher

Abstract

Quantum coherence has been considered as a resource for quantum information process in recent years. Sharing the quantum resource distantly is a precondition for quantum communication. In this paper, we explore the quantum coherence properties of the prepared state starting from initially incoherent thermal light source. It is shown that the quantum coherence is directly proportional to the dimension of Hilbert space and therefore employ the orbital angular momentum (OAM) to encode resources. The distribution of biphoton thermal OAM state via the one-sided noisy channel (non-Kolmogorov turbulent atmosphere) is then investigated. It is found that the prepared OAM state can have large amount of quantum coherence, which is maximized when the thermal source is completely incoherent. The turbulence effects on quantum coherence are studied and compared to those on the fidelity and quantum channel capacity. Contrasting to the monotonic decay, the dynamics of coherence displays a peak during the propagation and the mechanism behind is presented. Finally, the dynamics of quantum thermal state can be more robust than that of Bell-like pure state since more interference can be induced. We believe our results is of importance to OAM quantum communication using quantum coherence as a resource.

DOI
10.1364/oe.456604

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Quantum coherence has been considered as a resource for quantum information process in recent years. Sharing the quantum resource distantly is a precondition for quantum communication. In this paper, we explore the quantum coherence properties of the prepared state starting from initially incoherent thermal light source. It is shown that the quantum coherence is directly proportional to the dimension of Hilbert space and therefore employ the orbital angular momentum (OAM) to encode resources. The distribution of biphoton thermal OAM state via the one-sided noisy channel (non-Kolmogorov turbulent atmosphere) is then investigated. It is found that the prepared OAM state can have large amount of quantum coherence, which is maximized when the thermal source is completely incoherent. The turbulence effects on quantum coherence are studied and compared to those on the fidelity and quantum channel capacity. Contrasting to the monotonic decay, the dynamics of coherence displays a peak during the propagation and the mechanism behind is presented. Finally, the dynamics of quantum thermal state can be more robust than that of Bell-like pure state since more interference can be induced. We believe our results is of importance to OAM quantum communication using quantum coherence as a resource.
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.
Free-space optical communication based on orbital angular momentum (OAM) offers advantages such as high security, large information capacity, and high-speed transmission. However, turbulence can induce random perturbations to the wavefront, thereby affecting communication performance. Hence, accurately measuring turbulence intensity is crucial. We delve into the quantum Fisher information (QFI) of the spatial coherence length, a pivotal parameter in atmospheric turbulence. Within the framework of free-space optical channels, we conduct a comprehensive analysis of the QFI in models encompassing both single and biphoton systems. As photons propagate through free space, the QFI regarding turbulence parameter initially increases and then decreases, due to the coupling and decoherence between the photons and turbulence. Increasing the number of OAM modes can significantly enhance the QFI regarding turbulence parameters. We considered situations closer to practical preparation, our results indicate that the impact of entanglement on estimation precision depends on the purity of the prepared entangled state. Moreover, we discuss and compare the variations in the QFI of various parameters upon considering backward scattering (BS). We believe our work is the first theoretical attempt towards the exploration of estimating the turbulence parameter via QFI.
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.
We study the propagations of quantum resources encoded in orbital angular momenta of two photons via the turbulent maritime atmosphere. The decay characteristics of entanglement, discord and coherence are studied for the cases of increasing propagation distance, different azimuthal quantum numbers, inner scales of turbulence and wavelengths of light source. We find that the entanglement does not suffer sudden vanishing for the one-side turbulent channels case while entanglement disappears nonasymptotically for a general case of two-side different turbulent channels similar to the specific case of two-side identical turbulent channels. Entanglement, discord and coherence have quite different decay laws and coherence possesses more robustness against the turbulence than entanglement and discord. Our results show that larger azimuthal quantum numbers and larger wavelength of light source may boost the quality of distributions of quantum resources in turbulent maritime atmosphere.
One of the most important properties of orbital angular momentum (OAM) of photons is that the Hilbert space required to describe a general quantum state is infinite dimensional. In principle, this could allow for encoding arbitrarily large amounts of quantum information per photon, but in practice, this potential is limited by decoherence and errors. To determine whether photons with OAM are suitable for quantum communication, we numerically simulated their passage through a turbulent atmosphere and the resulting errors. We also proposed an encoding scheme to protect the photons from these errors, and characterized its effectiveness by the channel fidelity.
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.