Z. Hradil, J. Summhammer, H. Rauch
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations. The proposed approach handles the noisy data corresponding to realistic incomplete observation with finite resolution.
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The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has greatly diminished the applicability of estimation theory in many practical implementations. The Holevo Cramer-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multi-parameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimisation over multiple variables. In this work, w…
We scrutinize the effects of non-ideal data acquisition on the homodyne tomograms of photon quantum states. The presence of a weight function, schematizing the effects of the finite thickness of the probing beam or equivalently noise, only affects the state reconstruction procedure by a normalization constant. The results are extended to a discrete mesh and show that quantum tomography is robust under incomplete and approximate knowledge of tomograms.
We introduce the quantum indirect estimation theory, which provides a general framework to address the problem of which ensemble averages can be estimated by means of an available set of measuring apparatuses, e. g. estimate the ensemble average of an observable by measuring other observable. A main ingredient in this approach is that of informationally complete (infocomplete in short) measurements, which allow to estimate the ensemble average of any arbitrary system operator, as for quantum tomography. This naturally leads to the more stringent concept of AB-informationally complete measureme…
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterody…
The precision limit in quantum state tomography is of great interest not only to practical applications but also to foundational studies. However, little is known about this subject in the multiparameter setting even theoretically due to the subtle information tradeoff among incompatible observables. In the case of a qubit, the theoretic precision limit was determined by Hayashi as well as Gill and Massar, but attaining the precision limit in experiments has remained a challenging task. Here we report the first experiment which achieves this precision limit in adaptive quantum state tomography…
It is well known that quantum mechanics is incompatible with local realistic theories. Svetlichny showed, through the development of a Bell-like inequality, that quantum mechanics is also incompatible with a restricted class of nonlocal realistic theories for three particles where any two-body nonlocal correlations are allowed [Phys. Rev. D 35, 3066 (1987)]. In the present work, we experimentally generate three-photon GHZ states to test Svetlichny's inequality. Our states are fully characterized by quantum state tomography using an overcomplete set of measurements and have a fidelity of (84+/-…
Quantum Machine Learning for State Tomography Using Classical Data
本文提出一种基于量子机器学习的量子态重构协议，仅使用经典测量数据在NISQ设备上实现高保真度重构，展示了在不同量子态上的成功应用。
Fast and Sure-ious Quantum Process Tomography
本文证明部分归一化是量子信道Choi态的精确保真度投影，从而将量子态层析算法提升为量子过程层析算法，并给出保真度投影最小二乘法的样本复杂度与数值优势。
Flow-based Phase-space Tomography of Continuous-variable Quantum States
研究连续变量量子态层析成像，提出基于流的QST-Flow框架，含QST-QFlow和QST-WFlow两个变体，能保持准概率归一化，通过多种态的基准测试展示其优势，为非经典玻色子系统相空间层析成像开辟新途径。
Flexible characterization techniques that identify and quantify experimental imperfections under realistic assumptions are crucial for the development of quantum computers. Gate set tomography is a characterization approach that simultaneously and self-consistently extracts a tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. Obtaining such a detailed picture of the experimental implementation is associated with high requirements on the number of sequences and their design, making gate set tomog…
Quantum measurement tomography with mini-batch stochastic gradient descent
本文提出基于小批量随机梯度下降的量子测量全息成像方法，适用于离散和连续变量量子系统，通过两种参数化方案提升重建保真度和抗噪声能力。
Interferometric measurement of the quadrature coherence scale using two replicas of a quantum optical state
本文提出一种利用量子态两个副本的线性干涉仪直接测量正交相干尺度的方法，无需完整态层析，扩展了Hong-Ou-Mandel效应，为非经典性评估提供了新途径。
Gradient-descent methods for fast quantum state tomography
针对量子态层析成像（QST）随量子比特数量增长的计算与实验复杂度问题，提出梯度下降（GD）后处理算法，通过多种密度矩阵参数化实现物理有效态重建，经基准测试在重建保真度、计算效率等方面优于现有方法，为噪声中等规模量子器件表征提供新途径。
Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices. This drives the search for tomographic methods that achieve greater accuracy. In the case of mixed states of a single 2-dimensional quantum system adaptive methods have been recently introduced that achieve the theoretical accuracy limit deduced by Hayashi and Gill and Massar. However, accurate estimation of higher-dimensional quantum states remains poorly understood. This is mainly due to the existence of incompatible observables, which makes multiparameter estimation difficult. Here we pres…
Bayesian approach to simultaneous quantum multiparameter estimation with finite data
本研究提出一种基于Personick方法的贝叶斯框架，通过极小极大优化得到有限数据下量子多参数联合估计的优化投影测量，经量子比特示例验证了方法有效性。
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