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arXiv:2405.02812

Neural Network Enhanced Single-Photon Fock State Tomography

Hsien-Yi Hsieh, Yi-Ru Chen, Jingyu Ning, Hsun-Chung Wu, Hua Li Chen, Zi-Hao Shi, Po-Han Wang, Ole Steuernagel, Chien-Ming Wu, Ray‐Kuang Lee

Published May 5, 2024• 0 citations
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Abstract

Even though heralded single-photon sources have been generated routinely through the spontaneous parametric down conversion, vacuum and multiple photon states are unavoidably involved. With machine-learning, we report the experimental implementation of single-photon quantum state tomography by directly estimating target parameters. Compared to the Hanbury Brown and Twiss (HBT) measurements only with clicked events recorded, our neural network enhanced quantum state tomography characterizes the photon number distribution for all possible photon number states from the balanced homodyne detectors. By using the histogram-based architecture, a direct parameter estimation on the negativity in Wigner's quasi-probability phase space is demonstrated. Such a fast, robust, and precise quantum state tomography provides us a crucial diagnostic toolbox for the applications with single-photon Fock states and other non-Gaussisan quantum states.

DOI
10.48550/arxiv.2405.02812

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Even though heralded single-photon sources have been generated routinely through the spontaneous parametric down conversion, vacuum and multiple photon states are unavoidably involved. With machine-learning, we report the experimental implementation of single-photon quantum state tomography by directly estimating target parameters. Compared to the Hanbury Brown and Twiss (HBT) measurements only with clicked events recorded, our neural network enhanced quantum state tomography characterizes the photon number distribution for all possible photon number states from the balanced homodyne detectors. By using the histogram-based architecture, a direct parameter estimation on the negativity in Wigner's quasi-probability phase space is demonstrated. Such a fast, robust, and precise quantum state tomography provides us a crucial diagnostic toolbox for the applications with single-photon Fock states and other non-Gaussisan quantum states.
Even though heralded single-photon sources have been generated routinely through spontaneous parametric down conversion, vacuum and multiple photon states are unavoidably involved. With machine learning, we report the experimental implementation of photon number state tomography by directly estimating target parameters. Compared to the Hanbury Brown and Twiss measurements only with clicked events recorded, our neural-network-enhanced quantum-state tomography characterizes the photon number distribution for all possible photon number states from the balanced homodyne detectors. By using the histogram-based architecture, a direct parameter estimation on the negativity in Wigner's quasiprobability phase space is demonstrated. Such a fast, robust, and precise quantum-state tomography provides us a crucial diagnostic toolbox for the applications with incoherent mixture of Fock states.
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Summary form only given. The single photon Fock state is one of the most fundamental states of the light field. It is highly non-classical and reveals the wave-particle duality of light most strikingly. Its marginal distributions are of non-Gaussian shape and its Wigner function exhibits a strong negativity around the origin of phase space. Although the reconstruction of the Fock state has already been performed for the motional state of trapped beryllium ions, in the optical domain this task has not been resolved so far, the main difficulty being the lack of coherent single-photon sources. We present results of applying the technique of optical homodyne tomography to the single photon Fock state prepared by conditional measurements on a photon pair produced in parametric down conversion.
Quantum state engineering and state characterization is a key task in quantum information processing in both discrete and continuous variable systems in the optical domain. In particular, quantum states with non-Gaussian (i.e., non-positive) Wigner quasiprobability distribution functions are crucial to universal, fault-tolerant quantum computing with continuous variables. In this talk, we present our recent results on single-photon Fock state tomography using Photon-Number-Resolving (PNR) measurements. We generated a highly pure narrow-band single-photon Fock state by heralding cavity-enhanced spontaneous-parametric-downconversion from a PPKTP optical parametric oscillator. The Wigner function was reconstructed with photon statistics obtained using superconducting transition-edge sensors with an overall system efficiency of 58(2)%. We then discuss quantum state engineering for pure displaced single-photon Fock states, optical cat states, and approximate GKP states using coherent states and single-photon states along with linear optics and PNR measurements. We report our experimental progress for the same.