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Zhongguo kexue. Wulixue Lixue Tianwenxue

Logical Bell state measurement for photon system in momentum and polarization degrees of freedom

Xiang-Xi LI, Ji QI, Zhe YANG, Rui‐Yang Yuan, Bao‐Cang Ren

Published Jul 11, 2024• 0 citations
Publisher

Abstract

Quantum logic coding efficiently enhances the noise immunity of quantum systems. A quantum logical qubit using multiple degrees of freedom (DOFs) of a photon is concise, and it can reduce resource consumption compared with a quantum logical qubit using multiple photons in one DOF. In this study, two logical Bell state measurement schemes are proposed for photon systems in momentum and polarization DOFs with linear optical elements, namely, momentum polarization logical Bell state measurement assisted by W-state and self-assisted momentum polarization logical Bell state measurement. In the first scheme, parity measurements on momentum and polarization DOFs are performed simultaneously using an auxiliary four-photon W-state. The even-parity logical Bell states can be distinguished by photon detector results, resulting in a success rate of 12.5%. The second scheme does not require an auxiliary entangled photon state, and the even-parity logical Bell states can be completely distinguished by simple linear optical elements and photon detector results with a success rate of 50%. These two linear optical momentum polarization logical Bell state measurement schemes are easier to implement experimentally than the nonlinear optical schemes, and their applications in quantum communication protocols are crucial.

DOI
10.1360/sspma-2023-0439

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Quantum logic coding efficiently enhances the noise immunity of quantum systems. A quantum logical qubit using multiple degrees of freedom (DOFs) of a photon is concise, and it can reduce resource consumption compared with a quantum logical qubit using multiple photons in one DOF. In this study, two logical Bell state measurement schemes are proposed for photon systems in momentum and polarization DOFs with linear optical elements, namely, momentum polarization logical Bell state measurement assisted by W-state and self-assisted momentum polarization logical Bell state measurement. In the first scheme, parity measurements on momentum and polarization DOFs are performed simultaneously using an auxiliary four-photon W-state. The even-parity logical Bell states can be distinguished by photon detector results, resulting in a success rate of 12.5%. The second scheme does not require an auxiliary entangled photon state, and the even-parity logical Bell states can be completely distinguished by simple linear optical elements and photon detector results with a success rate of 50%. These two linear optical momentum polarization logical Bell state measurement schemes are easier to implement experimentally than the nonlinear optical schemes, and their applications in quantum communication protocols are crucial.
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.
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.
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.
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.
Fault tolerance is essential for scalable quantum technologies and is enabled by quantum error-correction codes. Bell-state measurements (BSMs) are a fundamental building block for modern quantum technologies such as measurement-based quantum computation and fusion-based quantum computation, as well as quantum networks. Therefore, performing BSMs on error-corrected qubits is a necessary step for achieving fault tolerance in these applications. In this work, we realise a logical BSM using linear optics, based on a two-qubit repetition code, an instance of a quantum parity code that allows detection of bit-flip errors, and experimentally achieve a mean success probability of (70.8 +/- 0.4)%. While standard linear-optical BSMs are fundamentally limited to a maximum success probability of 50%, this increased success probability enables higher secure key rates in quantum communication and facilitates the generation of large graph states for quantum computation. Since fault-tolerant schemes require error-correction codes regardless, this improvement comes at no additional resource overhead. Our results demonstrate that error-correction codes can be used to surpass the linear-optics limit of BSMs, which is an important step towards practical, fault-tolerant, and scalable photonic quantum technologies.
Bell state measurement is vital to quantum information technology. Conventional linear optical elements, however, cannot fully distinguish all polarization Bell states without assisting of additional degrees of freedom. Leveraging on a pair of binary-pixel metasurfaces, we demonstrate direct measurement of all four polarization Bell states. Each metasurface is designed to produce two output modes that linearly superpose three Bell states in the coincidence counting measurement. By rotating the polarizers, the coincidence counting measurement achieves a tunable anticorrelation between one and the other two Bell states, achieving Bell state detection efficiency of 75% in a single measurement. Complete and deterministic Bell state measurement is further realized by performing two measurements. Our work shows the advantage of utilization of metasurfaces in quantum detection schemes and is of great applicative interest for quantum dense coding, entanglement swapping, quantum teleportation protocols, and novel quantum information processing tasks.