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Frontiers in Optics

Automated Quantification of Error Sources in Quantum State Tomography of Time-bin Entangled Photons

Junpei Oba, Hsin-Pin Lo, Yasuhiro Yamada, Takayuki Matsui, Takuya Ikuta, Yuya Yonezu, Toshimori Honjo, Seiji Kajita, Hiroki Takesue

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We present a model-based framework that quantifies error sources by optimizing model parameters to reproduce an experimental density matrix, successfully attributing 87% errors in the experiment of the time-bin entangled photon-pair generation.
DOI
10.1364/fio.2025.fth3c.5

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Abstract High-quality quantum state generation is essential for advanced quantum information processing, including quantum communication, quantum sensing, and quantum computing. In realistic experiments, however, the generated quantum state is degraded by multiple experimental error sources whose individual contributions are often difficult to quantify and calibrate. Quantum state tomography (QST) provides experimental access to the resulting density matrix, but it does not by itself attribute observed deviations to specific error sources. To address this problem, we propose an automated method for quantifying error sources by combining simulation and parameter optimization, in which a parametrized simulator of state preparation and measurement is optimized so that the simulated density matrix best fits the experimentally reconstructed density matrix obtained via QST. We focus on the experimental generation of time-bin entangled photon pairs, for which we model the relevant error sources and simulate the density matrix with adjustable model parameters, thereby optimizing the parameters and minimizing the trace distance to the experimental data. Optimization of the parameters reduced the trace distance from 0.177 to 0.024, indicating that our modeled error sources explain 86% of the errors. Reducing the predicted error sources improves the state quality, consistent with our predictions and thus validating the proposed method. The proposed framework provides a practical route to automated, quantitative error attribution and calibration directly from experimental QST data.
We present a comprehensive framework for quantum state tomography of time-bin qudits sent through a fiber. Starting from basic assumptions, we define a positive-operator valued measure which is then applied to the quantum state reconstruction problem. A realistic scenario is considered where the time uncertainty of the detector is treated as a source of experimental noise. The performance of the quantum tomography framework is examined through a series of numerical simulations conducted for different parameters describing the apparatus. The quality of state recovery, quantified by the notion of minimum fidelity, is depicted on graphs for a range of fiber lengths. Special attention is paid to relative phase reconstruction for qubits and qutrits. The results present relevant interdependence between the fiber length and the detector jitter.
In this paper, we propose a method of dark count correction in quantum state tomography of entangled photon pairs. The framework is based on a linear model of dark counts, which is imposed on the measurement formalism. The method is tested on empirical data derived from an experiment on polarization-entangled photons. We demonstrate that the numerical approach to dark count correction guarantees more reliable state reconstruction compared with standard estimation. Most importantly, however, the conceptually simple theoretical approach proves to be more efficient at entanglement quantification than experimental techniques.
Quantum state tomography (QST) is an essential tool for characterizing an unknown quantum state. Recently, QST has been performed for entangled qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we propose a QST for time-bin qudits, with which the number of measurement settings scales linearly with dimension d . Using the proposed scheme, we performed QST for a four-dimensional time-bin maximally entangled state with 16 measurement settings. We successfully reconstructed the density matrix of the entangled qudits, with which the average fidelity of the state was calculated to be 0.950.
The entangled pairs of single photons are best described by density matrices that capture the complete description of their state. The quantum state can be disturbed from the idealist pure description due to imperfections and nonidealities. Therefore, it is important to completely measure the state of these pairs. This is a systematic protocol called quantum state tomography that achieves this measurement. In one such experiment, the entangled pair is measured along different directions by projecting it onto a series of measurement bases. The measured outcomes are then assembled with an algorithm to reproduce the density matrix. This procedure is the subject of the ninth chapter.