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Europhysics Letters (EPL)

The analysis of efficiency for high-dimensional quantum secure direct communications under atmospheric turbulence

Jia-Lei Niu, Xin-Chang Liu

Published Mar 2, 2022• 5 citations
Publisher

Abstract

Abstract Recently, there is a tremendous attention on the high-dimensional quantum information processing using the orbital angular momentum (OAM) of photons. It provides an efficient method to increase the capacity of quantum channel. However, OAM is very vulnerable to atmospheric turbulence, resulting in phase distortion and, therefore, leading to information leakage during quantum communications. On the other hand, quantum secure direct communications (QSDC) define an efficient way of information exchange through quantum channels directly. Here in this work, by combining the applications of OAM states of photons as the information carrier with the QSDC, we analyze the performance of the high-dimensional quantum secure direct communication protocol based on encoding the information on the single photon OAM state under the condition of free space channel. Numerically, we discussed the performance of OAM states QSDC under atmospheric turbulence, and mainly calculated the influence of cross-talk caused by phase fluctuation on the system. We draw the conclusion that under the weak turbulence, when the beam waist and the Fried parameter r become comparable, the information capacity will decrease sharply.

DOI
10.1209/0295-5075/ac59f0

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Abstract Recently, there is a tremendous attention on the high-dimensional quantum information processing using the orbital angular momentum (OAM) of photons. It provides an efficient method to increase the capacity of quantum channel. However, OAM is very vulnerable to atmospheric turbulence, resulting in phase distortion and, therefore, leading to information leakage during quantum communications. On the other hand, quantum secure direct communications (QSDC) define an efficient way of information exchange through quantum channels directly. Here in this work, by combining the applications of OAM states of photons as the information carrier with the QSDC, we analyze the performance of the high-dimensional quantum secure direct communication protocol based on encoding the information on the single photon OAM state under the condition of free space channel. Numerically, we discussed the performance of OAM states QSDC under atmospheric turbulence, and mainly calculated the influence of cross-talk caused by phase fluctuation on the system. We draw the conclusion that under the weak turbulence, when the beam waist and the Fried parameter r become comparable, the information capacity will decrease sharply.
Quantum secure direct communication (QSDC) with the feature of allowing secret messages to be communicated directly over quantum channels has two approaches including discrete variable and continuous variable (CV). Among of them, the CVQSDC system indicates the advantages of high secrecy capacity and low experimental cost. As the number of eigenstates is unbounded, the orbital angular momentum (OAM) is an efficient method to increase the secrecy capacity in a CVQSDC system. However, OAM is very vulnerable to atmospheric turbulence, resulting in a phase distortion quantum state. In this work, we propose a CVQSDC protocol with OAM multiplexing, and reveal how the channel parameters, especially transmittance and excess noise, are influenced by atmospheric effects through the simulation experiment. On this basis, the security of the system is further analyzed and the secrecy capacity calculated. The results indicated that the increase in turbulence intensity leads to enhanced crosstalk between the OAM angular modes, which in turn leads to a decrease in the effective transmittance and an increase in the excess noise. Meanwhile, the results also showed that the secrecy capacity decreases with the increase of transmission distance, atmospheric turbulence intensity, and angular mode; in addition, OAM multiplexing can obtain more secrecy capacity compared with a single link.
The existing quantum secure direct communication (QSDC) protocols mainly make use of the spin angular momentum and entangled photons, to realize direct transmission of confidential information. But those protocols' capacity is low, only one-bit information. On the other hand, the orbital angular momentum (OAM) of a photon can be theoretically evaluated from minus infinity to infinity, and the angular momentum states of different orbits are orthogonal to each other. Given that, in this paper, we propose a quantum secure direct communication scheme based on OAM. Specifically, taking OAM of photons as the information carrier, the data of information is segmented and high-capacity coding in quantum secure direct communication is realized through the segmentation of sector states.
Higher channel capacity and noise elimination are the key requirements for the implementation of long-distance quantum communication. As the additional degrees of freedom (DoF) of photons can be employed to achieve higher channel capacity and security beyond the polarizations DoF of photons, the photonic qubits are always employed as the flying qubits in quantum communication and quantum information processing. Here, exploiting the multiple DoFs of photons, we present an efficient quantum secure direct communication protocol based on the coding and manipulation of qubits on both the polarization and the orbital angular momentum of photons. Also, the numerical simulation is studied to further clarify the improvement of the channel capacity and the security. It is found that the channel capacity and the error rate (caused by eavesdropping) of the QSDC protocol which encoded on the polarization DoF and the OAM DoF is significantly higher than that of coding on only polarization DoF. We believe this work could provide more evidence for the applications of higher-dimensional qubits in quantum information science.
Orbital angular momentum (OAM) states of photons span a high-dimensional Hilbert space, and by using it, higher information capacity and enhanced security can be achieved for both classical communication and quantum key distribution. In this work, we propose a feasible basis-independent encoding scheme for OAM states and show its application in high-dimensional quantum secure direct communication, which enables direct transmission of meaningful messages, in addition to random secret key establishing. Imperfections of optical components may reduce the efficiency of the encoding scheme and, thus, the channel capacity. We discuss the optimal input distribution under realistic conditions to achieve maximal mutual information and an alternative solution using a different set of mutually unbiased bases in the case of a prime-dimensional quantum system.
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.
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.