Practical Bayesian tomography

We report an experimental realization of adaptive Bayesian quantum state tomography for twoqubit states. Our implementation is based on the adaptive experimental design strategy proposed in [1] and provides an optimal measurement approach in terms of the information gain. We address the practical questions, which one faces in any experimental application: the influence of technical noise, and behavior of the tomographic algorithm for an easy to implement class of factorized measurements. In an experiment with polarization states of entangled photon pairs we observe a lower instrumental noise floor and superior reconstruction accuracy for nearly-pure states of the adaptive protocol compared to a non-adaptive. At the same time we show, that for the mixed states the restriction to factorized measurements results in no advantage for adaptive measurements, so general measurements have to be used.

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“…based on a particular decoherence model for a given system. For a recent recipe of constructing useful informative priors, see [34].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Experimental adaptive quantum tomography of two-qubit states

et al. 2016

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“…Recently, methods employed in classical statistical-model selection were used to localize the signal (see, for example, refs 23, 24, 25, 26, 27, 28). These methods involve the consideration of the popular Akaike criterion and the Bayesian information criterion to penalize the likelihood function for the problem and restrict models for up to a certain number of parameters.…”

mentioning

confidence: 99%

Crystallizing highly-likely subspaces that contain an unknown quantum state of light

Teo

Mogilevtsev

Mikhalychev

et al. 2016

Sci Rep

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In continuous-variable tomography, with finite data and limited computation resources, reconstruction of a quantum state of light is performed on a finite-dimensional subspace. In principle, the data themselves encode all information about the relevant subspace that physically contains the state. We provide a straightforward and numerically feasible procedure to uniquely determine the appropriate reconstruction subspace by extracting this information directly from the data for any given unknown quantum state of light and measurement scheme. This procedure makes use of the celebrated statistical principle of maximum likelihood, along with other validation tools, to grow an appropriate seed subspace into the optimal reconstruction subspace, much like the nucleation of a seed into a crystal. Apart from using the available measurement data, no other assumptions about the source or preconceived parametric model subspaces are invoked. This ensures that no spurious reconstruction artifacts are present in state reconstruction as a result of inappropriate choices of the reconstruction subspace. The procedure can be understood as the maximum-likelihood reconstruction for quantum subspaces, which is an analog to, and fully compatible with that for quantum states.

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“…Our implementation follows closely the approaches used in [16] and [22]. For a Bayesian update scheme, we start with an initial prior probability density p(ρ) over feasible state space (usually uninformed due to the absence of additional knowledge, resulting in a uniform prior).…”

Section: Non-adaptive Bayesian Tomographymentioning

confidence: 99%

Coarse-graining in retrodictive quantum state tomography

2019

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Quantum state tomography (QST) is a combination of experimental and data-processing methods for complete characterisation of a quantum system. However, it often operates in the highly idealised scenario of assuming perfect measurements. The errors implied by such an approach are entwined with other imperfections relating to the information processing protocol or application of interest. We consider the problem of retrodicting the quantum state of a system, existing prior to the application of random but known phase errors, allowing those errors to be separated and removed. The continuously random nature of the errors implies that effective measurement operators are never repeated. This is a feature of many physical scenarios such as photonic cluster state generation and has a drastically adverse effect on data-processing times. Utilising state-of-the-art approaches to quantum state tomography, we describe a novel and effective method to account for these errors, resulting in improved reconstruction fidelities. Furthermore, we show how the use of 'coarse-graining' introduced in this work can substantially reduce the computation time in several maximum likelihood algorithms, for only modest sacrifices in fidelity.

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Practical Bayesian tomography

Cited by 101 publications

References 60 publications

Experimental adaptive quantum tomography of two-qubit states

Experimental adaptive quantum tomography of two-qubit states

Crystallizing highly-likely subspaces that contain an unknown quantum state of light

Coarse-graining in retrodictive quantum state tomography

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