• Corpus ID: 235265955

Efficient adaptive MCMC implementation for Pseudo-Bayesian quantum tomography

  title={Efficient adaptive MCMC implementation for Pseudo-Bayesian quantum tomography},
  author={T. T. Mai},
We revisit the Pseudo-Bayesian approach to the problem of estimating density matrix in quantum state tomography in this paper. Pseudo-Bayesian inference has been shown to offer a powerful paradign for quantum tomography with attractive theoretical and empirical results. However, the computation of (Pseudo-)Bayesian estimators, due to sampling from complex and high-dimensional distribution, pose significant challenges that hampers their usages in practical settings. To overcome this problem, we… 

Figures from this paper


A practical and efficient approach for Bayesian quantum state estimation
An improved, self-contained approach for Bayesian quantum state estimation that relies on highly efficient preconditioned Crank--Nicolson sampling and a pseudo-likelihood is introduced.
Bayesian inference for quantum state tomography
A Bayesian approach to the problem of estimating density matrices in quantum state tomography, where a study of the convergence of the Monte Carlo Markov Chain algorithm is given, including a comparison with other estimation methods, such as maximum likelihood estimation and linear inversion.
Pseudo-Bayesian quantum tomography with rank-adaptation
Abstract Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the
An invitation to quantum tomography
We describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on
3 Maximum-Likelihood Methods in Quantum Mechanics
Maximum Likelihood estimation is a versatile tool covering wide range of applications, but its benefits are apparent particularly in the quantum domain. For a given set of measurements, the most
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
Quantum state tomography: Mean squared error matters, bias does not
Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may
Reconstruction of Quantum States of Spin Systems : From Quantum Bayesian Inference to Quantum Tomography
We study in detail the reconstruction of spin-1 2 states and analyze the connection between (1) quantum Bayesian inference, (2) reconstruction via the Jaynes principle of maximum entropy, and (3)
Spectral thresholding quantum tomography for low rank states
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states,
Optimal large-scale quantum state tomography with Pauli measurements
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this