Adaptive Bayesian and frequentist data processing for quantum tomography

Frequentist and Bayesian Quantum Phase Estimation

Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cramèr-Rao bound, for instance, do not apply to Bayesian strategies and vice-versa. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixe…

受驱二能级量子系统跃迁频率的贝叶斯估计量与频率派估计量

Bayesian and frequentist estimators for the transition frequency of a driven two-level quantum system

针对受外部旋转磁场驱动的二能级量子系统，采用贝叶斯与频率派方法估计未知跃迁频率，提出代价函数优化经典Fisher信息，并证明贝叶斯最小均方误差估计量能提供无歧义估计。

Contrasting Implications of the Frequentist and Bayesian Interpretations of Probability when Applied to Quantum Mechanics Theory

An examination is made of the differing implications from applying the two mainstream interpretations of probability, frequentist and Bayesian, to QM (quantum mechanics) theory for the Bohm-EPR experiment. The joint probability distribution for the possible spin outcomes for two particles with coupled spins is examined. Contrasting conclusions are made: (i) Under the frequentist interpretation, the QM spin distribution implies a widely-discussed non-locality because probabilistic conditioning on a spin measurement is viewed as corresponding to a causal influence. Under the Bayesian interpretat…

Experimental Adaptive Bayesian Tomography

We report an experimental realization of an adaptive quantum state tomography protocol. Our method takes advantage of a Bayesian approach to statistical inference and is naturally tailored for adaptive strategies. For pure states we observe close to 1/N scaling of infidelity with overall number of registered events, while best non-adaptive protocols allow for $1/\sqrt{N}$ scaling only. Experiments are performed for polarization qubits, but the approach is readily adapted to any dimension.

Two-Qubit Hamiltonian Tomography by Bayesian Analysis of Noisy Data

We present an empirical strategy to determine the Hamiltonian dynamics of a two-qubit system using only initialization and measurement in a single fixed basis. Signal parameters are estimated from measurement data using Bayesian methods from which the underlying Hamiltonian is reconstructed, up to three unobservable phase factors. We extend the method to achieve full control Hamiltonian tomography for controllable systems via a multi-step approach. The technique is demonstrated and evaluated by analyzing data from simulated experiments including projection noise.

Bayesian homodyne and heterodyne tomography

Continuous-variable (CV) photonic states are of increasing interest in quantum information science, bolstered by features such as deterministic resource state generation and error correction via bosonic codes. Data-efficient characterization methods will prove critical in the fine-tuning and maturation of such CV quantum technology. Although Bayesian inference offers appealing properties -- including uncertainty quantification and optimality in mean-squared error -- Bayesian methods have yet to be demonstrated for the tomography of arbitrary CV states. Here we introduce a complete Bayesian qua…