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Optics Express

Four-dimensional orbital angular momentum Bell-state measurement assisted by the auxiliary polarization and path degrees of freedom

Chaojie Wang, Yuanyuan Chen, Lixiang Chen

Published Aug 23, 2022• 11 citations
Publisher

Abstract

The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.

DOI
10.1364/oe.469704

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The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.
Bell state analysis (BSA) constitutes a foundational operation for distinguishing Bell states in numerous quantum information processing (QIP) protocols. In this work, we propose a theoretical scheme for realizing a perfect BSA tailored for polarized Bell states, with assistance from orbital angular momentum (OAM) and path entanglement. The linear-optics-based architecture for BSA circumvents the inherent limitations of nonlinear optical processes and enhances the robustness against environmental noise -- a major challenge in practical QIP implementations. The integrating hyperentanglement (combining polarization, OAM, and path degrees of freedom (DOFs)) raises the theoretical success probability to 100%, achieving deterministic BSA. This deterministic BSA scheme offers a promising route toward practical, high-performance QIP in photonic systems, leveraging current experimental techniques and addressing key limitations of existing methods.
We present a theoretical scheme for the complete Bell state measurement (BSM) for high-dimensional hyperentangled photons in polarization and path degrees of freedom (DOFs), in which the polarization entanglement is in two-dimensional Hilbert space and the path entanglement is in four-dimensional Hilbert space. This 2×4-dimensional photonic quantum system contains 64 mutually orthogonal high-dimensional hyperentangled Bell states, which can be unambiguously discriminated by using weak cross-Kerr nonlinearity, linear optical element, and single-photon detector. This is the first complete BSM scheme for high-dimensional hyperentangled photons in two DOFs assisted by the quantum nonlinear effect, and we also demonstrate its application in the quantum superdense coding protocol, which allows the transmission of log 2 64=6 bits of classical information via just sending one photon. Moreover, our scheme only requires the achievable small nonlinear phase shift, and it can provide new avenues for other BSM-based quantum information technologies involving photonic high-dimensional hyperentanglement.
With the assistance of auxiliary two-dimensional polarization entanglement, we theoretically present an efficient Bell state measurement (BSM) method for photonic four-dimensional entanglement in the path degree of freedom, in which just simple linear optical elements and common single-photon detectors are utilized. With this approach, the 16 mutually orthogonal four-dimensional path Bell states can be classified into eight distinguishable groups, which allows the transmission of 3 bits of classical information by just sending one photon in our quantum superdense coding protocol. Compared with previous quantum dense coding protocols that are also based on linear-optical BSM, our protocol has certain advantages and will be useful for other quantum communication protocols based on high-dimensional entanglement.
In this paper, we present an efficient scheme for the complete analysis of the four-dimensional Bell state of the photon system in the path degree of freedom, resorting to the weak cross-Kerr nonlinearity and linear optics. In our scheme, the measurements on two probe coherent states are used for obtaining the bit information of high-dimensional entanglement, and the linear optical elements and single-photon detectors are used for obtaining the relative phase information of high-dimensional entanglement. With these two independent processes, the 16 orthogonal four-dimensional path Bell states can be completely distinguished from each other. This simple and realizable scheme may have useful applications in the quantum information technology based on high-dimensional entanglement.
Hyperentangled state analysis is an important module in high-capacity quantum communication. We present a self-assisted deterministic hyperentangled-Bell-state analysis (HBSA) scheme for photon system entangled in three degrees of freedom (DOFs), where 64 polarization-double longitudinal momentum hyperentangled Bell states are completely distinguished. In this HBSA scheme, the four first longitudinal momentum Bell states are distinguished determinately by nondestructive first longitudinal momentum Bell state analyzer, which is constructed with cross-Kerr nonlinearity medium. The 16 second longitudinal momentum-polarization hyperentangled Bell states are distinguished determinately by self-assisted second longitudinal momentum-polarization hyperentangled Bell state analyzer using linear optical elements, where the first longitudinal momentum Bell state and time-bin entangled state are used as auxiliary. Using this self-assisted method, the application of nonlinear optical resource in HBSA scheme has been largely reduced, which makes this self-assisted deterministic HBSA scheme has potential application prospects in high-capacity quantum communication.
Twisted photons can in principle carry a discrete unbounded amount of orbital angular momentum (OAM), which are of great significance for quantum communication and fundamental tests of quantum theory. However, the methods for characterization of the OAM quantum states present a fundamental limit for miniaturization. Metasurfaces can exploit new degrees of freedom to manipulate optical fields beyond the capabilities of bulk optics, opening a broad range of novel and superior applications in quantum photonics. Here we present a scheme to reconstruct the density matrix of the OAM quantum states of single photons with all-dielectric metasurfaces composed of birefringent meta-atoms. We have also measured the Schmidt number of the OAM entanglement by the multiplexing of multiple degrees of freedom. Our work represents a step toward the practical application of quantum metadevices for the measurement of OAM quantum states in free-space quantum imaging and communications.