Experimental adaptive Bayesian tomography

Kravtsov, Konstantin; Straupe, S. S.; Radchenko, I. V.; Houlsby, Neil; Huszár, Ferenc; Kulik, S. P.

doi:10.1103/physreva.87.062122

Cited by 87 publications

(85 citation statements)

References 20 publications

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“…The latter ideas were implemented experimentally for a single parameter estimation [6,7]. Two recent experimental implementations [8,9] have demonstrated the quadratic enhancement in the accuracy of reconstruction, measured as the infidelity with the "true" state, for adaptive estimation of qubit states. The experiment in [8] relied on a single adaptive step: when half of the data are collected, the most likely state is estimated and the following measurements are performed in the eigenbasis of the estimated state.…”

Section: Introductionmentioning

confidence: 99%

Experimental adaptive quantum tomography of two-qubit states

et al. 2016

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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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Section: Introductionmentioning

confidence: 99%

Experimental adaptive quantum tomography of two-qubit states

et al. 2016

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“…We analyze the applicability of different sets of probe states for data-pattern tomography. For the chosen basis set, the efficiency of the reconstruction could be enhanced using, for example, the adaptive Bayesian procedure [19][20][21][22].…”

Section: Optimal Basis Setsmentioning

confidence: 99%

Data-pattern tomography of entangled states

2017

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We discuss the data-pattern tomography for reconstruction of entangled states of light. We show that for a moderate number of probe coherent states it is possible to achieve high accuracy of representation not only for single-mode states but also for two-mode entangled states. We analyze the stability of these representations to the noise and demonstrate the conservation of the purity and entanglement. Simulating the probe and signal measurements, we show that systematic error inherent for representation of realistic signal response with finite sets of responses from probe states still allows one to infer reliably the signal states preserving entanglement.

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“…The papers [12,5] compare Bayesian methods to other methods on simulated data. More recently, [30,19,31,38] discuss efficient algorithms for computing Bayesian estimators. Importantly, [9] showed that Bayesian method comes with natural error bars and is the most accurate scheme w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Pseudo-Bayesian quantum tomography with rank-adaptation

Mai

Alquier

2017

Journal of Statistical Planning and Inference

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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 good and reliable choices in estimating quantum states [9]. Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of 1-qubit state recovery. However, the problem of choosing prior distribution in the general case of n qubits is not straightforward. More importantly, the statistical performance of Bayesian type estimators have not been studied from a theoretical perspective yet. In this paper, we propose a novel prior for quantum states (density matrices), and we define pseudo-Bayesian estimators of the density matrix. Then, using PAC-Bayesian theorems [16], we derive rates of convergence for the posterior mean. The numerical performance of these estimators are tested on simulated and real datasets.

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Experimental adaptive Bayesian tomography

Cited by 87 publications

References 20 publications

Experimental adaptive quantum tomography of two-qubit states

Experimental adaptive quantum tomography of two-qubit states

Data-pattern tomography of entangled states

Pseudo-Bayesian quantum tomography with rank-adaptation

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