Classical simulation of high-dimensional entanglement by non-separable angular–radial modes

Liu, Shi-Long; Liu, Shikai; Yang, Chen; Xu, Zong; Li, Yin-Hai; Li, Yan; Zhou, Zhiyuan; Guo, Guang-Can; Shi, Bao‐Sen

doi:10.1364/oe.27.018363

Cited by 9 publications

(7 citation statements)

References 76 publications

(136 reference statements)

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“…Thus, it is possible to identify noise thresholds, for each dimension d , such that if exceeded the quantum‐to‐classical transition will emerge, making large systems behaving classically under Bell‐like tests. Experimental violation of generalized Bell inequalities have been achieved with energy–time entangled qutrits (

d = 3

qudit), with entangled radial and angular degrees of freedom of Laguerre–Gauss (LG) modes for qudits with dimension

2 \leq d \leq 10

and up to

d = 12

with entangled qudits encoded in the OAM degree of freedom . The larger violation of Bell inequalities gives also benefit on entanglement‐based device‐independent QKD protocols.…”

Section: Enlarging Hilbert Spaces: the More The Bettermentioning

confidence: 99%

High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

et al. 2019

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In recent years, there has been a rising interest in high‐dimensional quantum states and their impact on quantum communication. Indeed, the availability of an enlarged Hilbert space offers multiple advantages, from larger information capacity and increased noise resilience, to novel fundamental research possibilities in quantum physics. Multiple photonic degrees of freedom have been explored to generate high‐dimensional quantum states, both with bulk optics and integrated photonics. Furthermore, these quantum states have been propagated through various channels, for example, free‐space links, single‐mode, multicore, and multimode fibers, and also aquatic channels, experimentally demonstrating the theoretical advantages over 2D systems. Here, the state‐of‐the‐art on the generation, propagation, and detection of high‐dimensional quantum states is reviewed. Quantum communication with states living in d‐dimensional Hilbert spaces, qudits, yields great benefits. However, qudits generation, transmission, and detection is not a simple task to accomplish. This review presents the state‐of‐the‐art on the generation, propagation, and measurement of high‐dimensional quantum states, highlighting their advantages, issues, and future perspectives.

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d = 3

qudit), with entangled radial and angular degrees of freedom of Laguerre–Gauss (LG) modes for qudits with dimension

2 \leq d \leq 10

and up to

d = 12

with entangled qudits encoded in the OAM degree of freedom . The larger violation of Bell inequalities gives also benefit on entanglement‐based device‐independent QKD protocols.…”

Section: Enlarging Hilbert Spaces: the More The Bettermentioning

confidence: 99%

High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

et al. 2019

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“…Hence, here the dimensionality is decided only by the azimuthal index, while the radial index is chosen to achieve the same modal number, and therefore to ensure the modes propagate in an identical way [37,38]. In other words, the qudits is encoded using both transverse indices that completely define the transverse structure of LG modes [48,49].…”

Section: Methods and Resultsmentioning

confidence: 99%

Propagation-invariant high-dimensional orbital angular momentum states

Mao¹,

Ding²,

Rosales‐Guzmán³

et al. 2022

J. Opt.

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Photonic states encoded in spatial modes of paraxial light fields provide a promising platform for high-dimensional quantum information protocols and related studies, where several pioneering theoretical and experimental demonstrations have paved the path for future technologies. Crucially, critical issues encountered in free-space propagation still represent a major challenge. This is the case of asynchronous diffraction between spatial modes with different modal orders, which experience variations in their transverse structure upon free-space propagation. Here we address this issue by proposing an encoding method based on the use of Laguerre-Gaussian (LG) modes of the same modal order N to define a N + 1 dimensional space. Noteworthy, such modes endowed with orbital angular momentum (OAM) experience the same propagation aberrations featuring an identical Gouy phase and wavefront curvature. We demonstrate our proposal experimentally by using time-correlated-single-photon imaging combined with a digital propagation technique. Importantly, our technique allows to eliminate, without the use of imaging systems, all issues related to asynchronous diffraction, providing an accessible way to generate propagation-invariant OAM qudits for quantum optical protocols.

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“…While the eigenstates of OAM can be any integer, making it possible for high dimensional quantum-like states. [37,38] In 2019, a 10D nonseparable state is proposed, [39] exploiting both angular l and radial p indices of Laguerre-Gaussian modes; the generation could be used to emulate high-dimensional two particles entanglement by experimentally observing the violations of the Bell-CGLMP-like inequality.…”

Section: Introductionmentioning

confidence: 99%

Intra‐Cavity Laser Manipulation of High‐Dimensional Non‐Separable States

Hai,

Zhang,

Liu

et al. 2023

Laser & Photonics Reviews

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Non‐separable states of structured light have the analogous mathematical forms with quantum entanglement, which offer an effective way to simulate quantum process. However, the classical multi‐partite non‐separable states analogue to multi‐particle entanglements can only be controlled by bulky free‐space modulation of light through coupling multiple degrees of freedom (DoFs) with orbital angular momentum (OAM) to achieve high dimensionality and other DoFs to emulate multi‐parties. In this paper, a scheme is proposed to directly emit multi‐partite non‐separable states from a simple laser cavity to mimic multi‐particle quantum entanglement. Through manipulating three DoFs as OAM, polarization, and wavevector inside a laser cavity, the eight‐dimensional (8D) tripartite states and all Greenberger‐Horne‐Zeilinger (GHZ)‐like states can be generated and controlled on demand. In addition, an effective method is proposed to perform state tomography employing convolutional neural network (CNN), for measuring the generated GHZ‐like states with highest fidelity up to 95.11%. This work reveals a feasibility of intra‐cavity manipulation of high‐dimensional multipartite non‐separable states, opening a compact device for quantum‐classical analogy and paving the path for advanced quantum scenarios.

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Classical simulation of high-dimensional entanglement by non-separable angular–radial modes

Cited by 9 publications

References 76 publications

High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

Propagation-invariant high-dimensional orbital angular momentum states

Intra‐Cavity Laser Manipulation of High‐Dimensional Non‐Separable States

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