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arXiv:2511.17011

Bell state analysis using orbital angular momentum and path degrees of freedom

Zi-Long Yang, Shi-Wen He, Lin-Cheng Wang, Si-Tong Jin, Liu Lv, Xiao-Ming Xiu, Chong Li

quant-phSubmitted Nov 21, 2025• Announced Nov 24, 2025• 0 citations
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Abstract

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.

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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.
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.
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.
Hyperentangled Bell states analysis (HBSA) is an essential building block for certain hyper-parallel quantum information processing. We propose a complete and deterministic HBSA scheme encoded in spatial and polarization degrees of freedom (DOFs) of two-photon system assisted by a fixed frequency-based entanglement and a time interval DOF. The parity information the spatial-based and polarization-based hyper-entanglement can be distinguished by the distinct time intervals of the photon pairs, and the phase information can be distinguished by the detection signature. Compared with previous schemes, the number of the auxiliary entanglements is reduced from two to one by introducing time interval DOF. Moreover, the additional frequency and time interval DOFs suffer less from the collective channel noise.
Abstract We present an efficient scheme for the complete hyperentangled Bell state analysis (HBSA) of photon system with polarization and two longitudinal momentum degrees of freedom (DOFs), resorting to weak cross-Kerr nonlinearity, linear optical elements and single photon detectors. In the process of distinguishing the 64 hyperentangled Bell states in three DOFs, the self-assisted mechanism is embedded, which makes our scheme simple and realizable. Moreover, we have discussed the applications of this complete HBSA scheme for high-capacity quantum communication protocols that are based on photonic hyperentanglement in three DOFs.
Abstract We present a simple scheme for the complete analysis of hyperentangled Bell states in polarization and spatial-mode degrees of freedom (DOFs) assisted by time-bin–frequency hyperentanglement. In previous schemes of distinguishing the 16 hyperentangled Bell states, many non-linear interaction systems are widely used to construct a quantum gate, such as cross-Kerr non-linearity, quantum-dot spin in an optical microcavity and nitrogen-vacancy centers in a resonator. In our scheme, we utilize the time-bin and frequency DOFs of a photon system as the auxiliary DOFs to analyze polarization–spatial-mode hyperentangled Bell states, and the distinguishing principle is quite different from the former schemes that use the non-linear interactions. As the manipulation of time-bin and frequency DOFs of photons is efficient and feasible with current technology, this scheme will be useful for high-capacity quantum information processing based on hyperentanglement.
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.