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arXiv:2308.07067 · Nature Communications

Efficient characterizations of multiphoton states with an ultra-thin optical device

Kui An, Zilei Liu, Ting Zhang, Siqi Li, You Zhou, Xiao Yuan, Leiran Wang, Wenfu Zhang, Guoxi Wang, He Lu

Published May 10, 2024• 17 citations
arXivHTMLPDF

Abstract

Metasurface enables the generation and manipulation of multiphoton entanglement with flat optics, providing a more efficient platform for large-scale photonic quantum information processing. Here, we show that a single metasurface optical device would allow more efficient characterizations of multiphoton entangled states, such as shadow tomography, which generally requires fast and complicated control of optical setups to perform information-complete measurements, a demanding task using conventional optics. The compact and stable device here allows implementations of general positive operator valued measures with a reduced sample complexity and significantly alleviates the experimental complexity to implement shadow tomography. Integrating self-learning and calibration algorithms, we observe notable advantages in the reconstruction of multiphoton entanglement, including using fewer measurements, having higher accuracy, and being robust against experimental imperfections. Our work unveils the feasibility of metasurface as a favorable integrated optical device for efficient characterization of multiphoton entanglement, and sheds light on scalable photonic quantum technologies with ultra-thin optical devices.

DOI
10.1038/s41467-024-48213-4

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Metasurface enables the generation and manipulation of multiphoton entanglement with flat optics, providing a more efficient platform for large-scale photonic quantum information processing. Here, we show that a single metasurface optical device would allow more efficient characterizations of multiphoton entangled states, such as shadow tomography, which generally requires fast and complicated control of optical setups to perform information-complete measurements, a demanding task using conventional optics. The compact and stable device here allows implementations of general positive operator valued measures with a reduced sample complexity and significantly alleviates the experimental complexity to implement shadow tomography. Integrating self-learning and calibration algorithms, we observe notable advantages in the reconstruction of multiphoton entanglement, including using fewer measurements, having higher accuracy, and being robust against experimental imperfections. Our work unveils the feasibility of metasurface as a favorable integrated optical device for efficient characterization of multiphoton entanglement, and sheds light on scalable photonic quantum technologies with ultra-thin optical devices.
Metasurfaces based on resonant nanophotonic structures have enabled innovative types of flat-optics devices that often outperform the capabilities of bulk components, yet these advances remain largely unexplored for quantum applications. We show that nonclassical multiphoton interferences can be achieved at the subwavelength scale in all-dielectric metasurfaces. We simultaneously image multiple projections of quantum states with a single metasurface, enabling a robust reconstruction of amplitude, phase, coherence, and entanglement of multiphoton polarization-encoded states. One- and two-photon states are reconstructed through nonlocal photon correlation measurements with polarization-insensitive click detectors positioned after the metasurface, and the scalability to higher photon numbers is established theoretically. Our work illustrates the feasibility of ultrathin quantum metadevices for the manipulation and measurement of multiphoton quantum states, with applications in free-space quantum imaging and communications.
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Reconstructing the density matrix of the quantum state of photons through a tomographically complete set of measurements, known as quantum state tomography, is an essential task in nearly all applications of quantum science and technology, from quantum sensing to quantum communications. Recent advances in optical metasurfaces enable the design of ultrathin nanostructured optical elements performing such state tomography tasks, promising greater simplicity, miniaturization, and scalability. However, reported metasurfaces on this goal were limited to a small Hilbert dimension, e.g., polarization qubits or spatial qudits with only a few states. When scaling up to higher-dimensional qudit tomography problems, especially those involving spatial qudits, a natural question arises: whether a metasurface with randomized nanostructures is sufficient to perform such qudit tomography, achieving optimal conditions. In this work, we attempt to answer this question through a set of numerical experiments with random metasurfaces, utilizing large-scale simulations of over 16,000 distinct metasurfaces, each exceeding 200 wavelengths in size. We show that, with sufficient redundancy in the number of detectors, random metasurfaces perform reasonably well in quantum photonic spatial qudit tomography encoded in Hermite-Gaussian states for up to approximately 10 states. Furthermore, we discuss additional considerations for optimizing metasurfaces in multiphoton cases. Our work opens a pathway toward computationally efficient, miniaturized, and error-tolerant quantum measurement platforms.
Quantum state tomography is an essential tool for characterizing quantum systems and underpins nearly every experimental realization of quantum technologies. Conventional tomography relies on performing a sequence of projective measurements on many identical copies of a quantum state, requiring the measurement apparatus to be reconfigured between successive acquisitions. As the Hilbert-space dimension increases, the number of required measurements grows rapidly; in practice, additional overcomplete measurements are often performed to improve robustness to experimental imperfections. Here, we introduce a tomography platform based on structured anisotropic media that performs informationally complete measurements of photonic polarization qubits within a single acquisition. The approach employs three liquid-crystal metasurfaces with spatially varying optic-axis orientations that transform the input polarization into a far-field distribution of discrete transverse-momentum modes. Each diffraction pattern uniquely determines the polarization state, enabling its reconstruction without sequential changes to the measurement apparatus. Unlike previous implementations, our scheme is intrinsically photon-number independent: the same optical device operates identically for arbitrary photon numbers, while the desired photon-number sector can be selected afterwards through post-selection of the corresponding nnn-fold coincidence events. We experimentally demonstrate single-frame quantum state tomography of both single- and two-photon polarization states, providing a simple and scalable route toward efficient quantum-state characterization.
Summary form only given. Measurements of quantum states of photons are conventionally performed with series of optical elements in bulk setups [1] or optical chips incorporating multiple tunable beam splitters. Here, we suggest and develop experimentally, for the first time to our knowledge, a new concept of quantum-polarization measurements with a single all-dielectric resonant metasurface [2]. The operating principle is presented in Fig. 1(a): A metasurface spatially splits different components of photon polarization states, which then enables full reconstruction of the photon state based on the photon correlations with simple polarization-insensitive single-photon detectors or EMCCD cameras. The subwavelength thin structure provides an ultimate miniaturization, and can facilitate quantum tomography by spatially-resolved imaging without a need for reconfiguration. Such parallel-detection approach promises not only better robustness and scalability, but also the possibility to study the dynamics of quantum states in real-time.