Practical Bayesian Tomography

@article{Granade2015PracticalBT,
  title={Practical Bayesian Tomography},
  author={C. Granade and J. Combes and D. Cory},
  journal={arXiv: Quantum Physics},
  year={2015}
}
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Husz\'ar and Houlsby and by Ferrie, to make Bayesian tomography… Expand
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References

SHOWING 1-10 OF 75 REFERENCES
Experimental Adaptive Bayesian Tomography
We discuss an experimental realization of an adaptive quantum state tomography protocol. The method we suggested and tested takes advantage of a Bayesian approach to statistical inference and isExpand
Quantum tomographic reconstruction with error bars: a Kalman filter approach
We present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. The method not only yields the maximum likelihood/optimal BayesianExpand
From quantum Bayesian inference to quantum tomography
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that theExpand
Practical and Reliable Error Bars in Quantum Tomography.
TLDR
This work proposes a practical yet robust method for obtaining error bars by introducing a novel representation of the output of the tomography procedure, the quantum error bars, and presents an algorithm for computing this representation and provides ready-to-use software. Expand
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)Expand
Reliable quantum state tomography.
TLDR
This work shows that quantum state tomography, together with an appropriate data analysis procedure, yields reliable and tight error bounds, specified in terms of confidence regions-a concept originating from classical statistics. Expand
On sequential Monte Carlo sampling methods for Bayesian filtering
TLDR
An overview of methods for sequential simulation from posterior distributions for discrete time dynamic models that are typically nonlinear and non-Gaussian, and how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature are shown. Expand
Adaptive Bayesian quantum tomography
In this letter we revisit the problem of optimal design of quantum tomographic experiments. In contrast to previous approaches where an optimal set of measurements is decided in advance of theExpand
Robust error bars for quantum tomography
In quantum tomography, a quantum state or process is estimated from the results of measurements on many identically prepared systems. Tomography can never identify the state or process exactly. AnyExpand
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
TLDR
A new theoretical analysis of compressed tomography is presented, based on the restricted isometry property for low-rank matrices, and it is shown that unknown low- rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. Expand
...
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2
3
4
5
...