# 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

#### Figures and Topics from this paper

#### 52 Citations

Adaptive quantum state tomography with iterative particle filtering

- Physics
- 2020

Several Bayesian estimation based heuristics have been developed to perform quantum state tomography (QST). Their ability to quantify uncertainties using region estimators and include a priori… Expand

Pseudo-Bayesian quantum tomography with rank-adaptation

- Mathematics, Physics
- 2017

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… Expand

A practical and efficient approach for Bayesian quantum state estimation

- Physics, Computer Science
- 2020

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. Expand

Practical adaptive quantum tomography *

- 2017

We introduce a fast and accurate heuristic for adaptive tomography that addressesmany of the limitations of priormethods. Previous approaches were either too computationally intensive or tailored to… Expand

Exponential families for Bayesian quantum process tomography

- Physics, Mathematics
- 2017

By associating the Choi matrix form of a completely positive, trace preserving (CPTP) map with a particular space of matrices with orthonormal columns, called a Stiefel manifold, we present a… Expand

Applied Bayesian Qubit State Tomography

- 2020

In this paper we present a simple Bayesian inference based single-stage quantum state tomography. Previous approaches such as maximum likelihood estimation are compared with Bayesian analysis and its… Expand

Practical and Reliable Error Bars in Quantum Tomography.

- Computer Science, Physics
- Physical review letters
- 2016

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

Fast state tomography with optimal error bounds

- Computer Science, Mathematics
- ArXiv
- 2018

The main result of this paper equips this point estimator with a rigorous, non-asymptotic confidence region expressed in terms of the trace distance. Expand

Adaptive Quantum State Tomography for Arbitrary Single Qubits

- Computer Science
- 2020

An adaptive particle filter based QST protocol that works efficiently for all single qubit states, due to its unabating perseverance to find the states' diagonal bases is presented. Expand

A comparative study of estimation methods in quantum tomography

- Physics, Mathematics
- 2019

As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate… Expand

#### References

SHOWING 1-10 OF 75 REFERENCES

Experimental Adaptive Bayesian Tomography

- 2015

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 is… Expand

Quantum tomographic reconstruction with error bars: a Kalman filter approach

- Physics
- 2009

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 Bayesian… Expand

From quantum Bayesian inference to quantum tomography

- Mathematics, Physics
- 1996

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 the… Expand

Practical and Reliable Error Bars in Quantum Tomography.

- Computer Science, Physics
- Physical review letters
- 2016

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

- 1998

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.

- Computer Science, Physics
- Physical review letters
- 2012

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

- Mathematics, Computer Science
- Stat. Comput.
- 2000

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

- Physics, Mathematics
- 2012

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 the… Expand

Robust error bars for quantum tomography

- Physics, Mathematics
- 2012

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. Any… Expand

Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators

- Computer Science, Physics
- 2012

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