scholarly journals Global convergence of diluted iterations in maximum-likelihood quantum tomography

2014 ◽  
Vol 14 (11&12) ◽  
pp. 966-980
Author(s):  
Doglas S. Goncalves ◽  
Marcia A. Gomes-Ruggiero ◽  
Carlile Lavor
Keyword(s):  
Maximum Likelihood ◽  
Global Convergence ◽  
Density Matrix ◽  
Quantum State ◽  
Maximum Likelihood Estimate ◽  
Quantum Tomography ◽  
Practical Implementation ◽  
Globally Convergent ◽  
State Tomography ◽  
New Interpretation

In this paper we address convergence issues of the Diluted $R \rho R$ algorithm \cite{rehacek2007}, used to obtain the maximum likelihood estimate for the density matrix in quantum state tomography. We give a new interpretation to the diluted $R \rho R$ iterations that allows us to prove the global convergence under weaker assumptions. Thus, we propose a new algorithm which is globally convergent and suitable for practical implementation.

scholarly journals Local solutions of maximum likelihood estimation in quantum state tomography

2012 ◽  
Vol 12 (9&10) ◽  
pp. 775-790
Author(s):  
Douglas S. Goncalves ◽  
Marcia A. Gomes-Ruggiero ◽  
Carlile Lavor ◽  
Osvaldo J. Farias ◽  
P. H. Souto Ribeiro
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Density Matrix ◽  
Quantum State ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Local Minima ◽  
Quantum State Tomography ◽  
Log Likelihood ◽  
State Tomography

Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace constraints is to parameterize the matrix to be reconstructed in order to ensure that it is physical. In this case, the negative log-likelihood function in terms of the parameters, may have several local minima. In various papers in the field, a source of errors in this process has been associated to the possibility that most of these local minima are not global, so that optimization methods could be trapped in the wrong minimum, leading to a wrong density matrix. Here we show that, for convex negative log-likelihood functions, all local minima of the unconstrained parameterized problem are global, thus any minimizer leads to the maximum likelihood estimation for the density matrix. We also discuss some practical sources of errors.

scholarly journals Quantum state tomography with incomplete data: Maximum entropy and variational quantum tomography

2013 ◽  
Vol 87 (5) ◽  
Author(s):  
D. S. Gonçalves ◽  
C. Lavor ◽  
M. A. Gomes-Ruggiero ◽  
A. T. Cesário ◽  
R. O. Vianna ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Quantum State ◽  
Incomplete Data ◽  
Quantum Tomography ◽  
Quantum State Tomography ◽  
State Tomography

scholarly journals Dynamic State Reconstruction of Quantum Systems Subject to Pure Decoherence

2020 ◽  
Vol 59 (11) ◽  
pp. 3646-3661
Author(s):  
Artur Czerwinski
Keyword(s):  
Quantum State ◽  
Open Systems ◽  
Initial Density ◽  
Quantum Tomography ◽  
Dynamic State ◽  
Reconstruction Method ◽  
State Reconstruction ◽  
Quantum State Tomography ◽  
Phase Damping ◽  
State Tomography

Abstract The article introduces efficient quantum state tomography schemes for qutrits and entangled qubits subject to pure decoherence. We implement the dynamic state reconstruction method for open systems sent through phase-damping channels, which was proposed in: Czerwinski and Jamiolkowski Open Syst. Inf. Dyn. 23, 1650019 (2016). In the present article we prove that two distinct observables measured at four different time instants suffice to reconstruct the initial density matrix of a qutrit with evolution given by a phase-damping channel. Furthermore, we generalize the approach in order to determine criteria for quantum tomography of entangled qubits. Finally, we prove two universal theorems concerning the number of observables required for quantum state tomography of qudits subject to pure decoherence. We believe that dynamic state reconstruction schemes bring advancement and novelty to quantum tomography since they utilize the Heisenberg representation and allow to define the measurements in time domain.

scholarly journals A scalable maximum likelihood method for quantum state tomography

2013 ◽  
Vol 15 (12) ◽  
pp. 125004 ◽  
Author(s):  
T Baumgratz ◽  
A Nüßeler ◽  
M Cramer ◽  
M B Plenio
Keyword(s):  
Maximum Likelihood ◽  
Quantum State ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Quantum State Tomography ◽  
State Tomography

scholarly journals Behavior of the maximum likelihood in quantum state tomography

2018 ◽  
Vol 20 (2) ◽  
pp. 023050 ◽  
Author(s):  
Travis L Scholten ◽  
Robin Blume-Kohout
Keyword(s):  
Maximum Likelihood ◽  
Quantum State ◽  
Quantum State Tomography ◽  
State Tomography

Quantum tomograph for measurement and characterization of quantum states of biphoton sources

2020 ◽  
pp. 20-26
Author(s):  
Dmitry N. Frolovtsev ◽  
Sergey A. Magnitskiy ◽  
Andrey V. Demin
Keyword(s):  
Density Matrix ◽  
Quantum State ◽  
Measurement Errors ◽  
Quantum Tomography ◽  
Statistical Characteristics ◽  
Light Sources ◽  
Matrix Elements ◽  
Experimental Implementation

The method and prototype of a device for characterizing of biphoton light sources based on spontaneous parametric downdonversion by quantum tomography are described. The prototype is an experimental implementation of a specialized quantum tomograph designed to measure the quantum polarization states of radiation generated by biphoton sources. Specially developed software will determine the statistical characteristics of the measured quantum state, calculate the tomographic and likelihood estimations of the density matrix, calculate the measurement errors of the density matrix elements and evaluate the quality of the quantum state of biphotons.

scholarly journals Attention-based Quantum Tomography

2021 ◽  
Author(s):  
Peter Junghwa Cha ◽  
Paul Ginsparg ◽  
Felix Wu ◽  
Juan Felipe Carrasquilla ◽  
Peter L. McMahon ◽  
...  
Keyword(s):  
Neural Network ◽  
Natural Language Processing ◽  
Natural Language ◽  
Density Matrix ◽  
Quantum State ◽  
Language Processing ◽  
Quantum Tomography ◽  
Neural Network Models ◽  
State Reconstruction ◽  
Quantum State Reconstruction

Abstract With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. There has been a growing interest in approaching the problem of quantum state reconstruction using generative neural network models. Here we propose the ``Attention-based Quantum Tomography'' (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. AQT is based on the model proposed in ``Attention is all you need" by Vaswani, et al. (2017) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for natural language processing captures the correlations among words in a sentence.

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