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Physical Review A

Neural-network-enhanced Fock-state tomography

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

Published Nov 7, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.110.053705

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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.
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.
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In order to leverage the full power of quantum noise squeezing with unavoidable decoherence, a complete understanding of the degradation in the purity of squeezed light is demanded. By implementing machine-learning architecture with a convolutional neural network, we illustrate a fast, robust, and precise quantum state tomography for continuous variables, through the experimentally measured data generated from the balanced homodyne detectors. Compared with the maximum likelihood estimation method, which suffers from time-consuming and overfitting problems, a well-trained machine fed with squeezed vacuum and squeezed thermal states can complete the task of reconstruction of the density matrix in less than one second. Moreover, the resulting fidelity remains as high as 0.99 even when the antisqueezing level is higher than 20 dB. Compared with the phase noise and loss mechanisms coupled from the environment and surrounding vacuum, experimentally, the degradation information is unveiled with machine learning for low and high noisy scenarios, i.e., with the antisqueezing levels at 12 dB and 18 dB, respectively. Our neural network enhanced quantum state tomography provides the metrics to give physical descriptions of every feature observed in the quantum state with a single scan measurement just by varying the local oscillator phase from 0 to 2π and paves a way of exploring large-scale quantum systems in real time.
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.