Process reconstruction from incomplete and/or inconsistent data

Quantum State Reconstruction From Incomplete Data

Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined only when measurements on infinite ensembles of identically prepared quantum systems are performed. But how one can estimate (guess) quantum state when just incomplete data are available (known)? What is the most reliable estimation based on a given measured data? What is the optimal measurement providing only a finite number of identically prepared quantum…

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when jus…

从噪声和不完整数据中学习纠缠准概率

Learning Entanglement Quasiprobability from Noisy and Incomplete Data

本文提出一种深度学习框架，直接从不完整的局部投影测量中重建纠缠准概率，减少全量子态重构的限制，实验验证显示在光子纠缠态中实现了更高效的纠缠检测。

Knowledge and ignorance in incomplete quantum state tomography

Quantum state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements does, as a rule, not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is the least-bias estimator, consistent with a given set of measurement data. This is equivalent to the joint consideration of our partial knowledge and ignorance about the ensemble to reconstruct its identity. An interesting st…

哈密顿量重构：关联矩阵与不完备算符基

Hamiltonian Reconstruction: the Correlation Matrix and Incomplete Operator Bases

本文研究关联矩阵哈密顿量重构对算符基选择的鲁棒性，提出欠完备基下的近似重构方案，并分析守恒量、对称性及温度对一维系统重构的影响。

Reconstruction of Markovian dynamics from untimed data

I develop a theoretical framework for inferring nonequilibrium equations of motion from incomplete experimental data. I focus on genuinely irreversible, Markovian processes, for which the incomplete data are given in the form of snapshots of the macrostate at different instances of the evolution, yet without any information about the timing of these snapshots. A reconstruction of the equation of motion must therefore be preceded by a reconstruction of time.