Adaptive quantum tomography in high dimensions

Pereira, L.; Zambrano, L.; Cortés-Vega, J.; Niklitschek, Sebastian; Delgado, A.

doi:10.1103/physreva.98.012339

Cited by 30 publications

(32 citation statements)

References 56 publications

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“…Moreover, one can extrapolate |V| that is adequate for the fidelity criterion from the asymptote so that the batch size of measurement outcomes could be properly increased to save training efforts. We notice that similar asymptotic behavior of R real has been generally observed in previous QST methods [55][56][57], thus the procedure here may also be adapted for them.…”

Section: Fidelity Estimationsupporting

confidence: 76%

Scalable quantum tomography with fidelity estimation

et al. 2020

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We propose a quantum tomography scheme for pure qudit systems which adopts random base measurements and generative learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic states. We prove the validity of the scheme theoretically, and we perform numerically simulated experiments on several target states including three typical quantum information states and randomly initiated states, demonstrating its efficiency and robustness. The number of replicas required by a certain convergence criterion grows in the manner of low-degree polynomial when the system scales, thus the scheme achieves high scalability that is crucial for practical quantum state tomography.

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Section: Fidelity Estimationsupporting

confidence: 76%

Scalable quantum tomography with fidelity estimation

et al. 2020

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“…From the theoretical and experimental point of view, it has been shown that a two-stage adaptive tomographic method achieves the quantum accuracy limit in the case of unknown mixed states of a single qubit 26 , 27 . Unfortunately, this result does not hold in the higher dimensional case 28 .…”

Section: Introductionmentioning

confidence: 93%

Estimation of pure quantum states in high dimension at the limit of quantum accuracy through complex optimization and statistical inference

Zambrano

Pereira

Niklitschek

et al. 2020

Sci Rep

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Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices. this drives the search for tomographic methods that achieve greater accuracy. in the case of mixed states of a single 2-dimensional quantum system adaptive methods have been recently introduced that achieve the theoretical accuracy limit deduced by Hayashi and Gill and Massar. However, accurate estimation of higher-dimensional quantum states remains poorly understood. This is mainly due to the existence of incompatible observables, which makes multiparameter estimation difficult. Here we present an adaptive tomographic method and show through numerical simulations that, after a few iterations, it is asymptotically approaching the fundamental Gill-Massar lower bound for the estimation accuracy of pure quantum states in high dimension. the method is based on a combination of stochastic optimization on the field of the complex numbers and statistical inference, exceeds the accuracy of any mixed-state tomographic method, and can be demonstrated with current experimental capabilities. the proposed method may lead to new developments in quantum metrology.

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“…Employing quantum state tomography (QST), one can obtain the complete information of a quantum state [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ]. Although higher dimensional pure states can be determined using just five measurement settings [ 15 ], the number of measurement configurations that are required in QST of a general d -dimensional quantum state scales badly with the dimension d .…”

Section: Introductionmentioning

confidence: 99%

Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

2020

Entropy

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An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et al., Nature Physics (2018), 14, 1032–1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.

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Adaptive quantum tomography in high dimensions

Cited by 30 publications

References 56 publications

Scalable quantum tomography with fidelity estimation

Scalable quantum tomography with fidelity estimation

Estimation of pure quantum states in high dimension at the limit of quantum accuracy through complex optimization and statistical inference

Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

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