Improved estimation accuracy of the 5-bases-based tomographic method

Zambrano, L.; Pereira, L.; Delgado, A.

doi:10.1103/physreva.100.022340

Cited by 12 publications

(14 citation statements)

References 44 publications

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“…Figure 1 displays, in logarithmic scale for both axes, mean and median of I(|ψ j ) as a function of the total ensemble size 3N used in the estimation process for a single quantum system with dimension d = 4 and for four randomly chosen unknown states in Ω 4 (from top to bottom). The left column compares the mean infidelity generated by the 3BB-QT method (solid red dots) and the IC5BB-QT method [50] (solid blue squares), a variation of the 5BB-QT method that achieves a higher accuracy. For the state at the first row of Fig.…”

Section: Accuracy Of the 3bb-qt Methodsmentioning

confidence: 99%

Estimation of pure states using three measurement bases

Zambrano

Pereira

Martínez

et al. 2020

Preprint

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We introduce a new method to estimate unknown pure d-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of 2d projectors are employed to generate a set of 2 d−1 possible states, the likelihood of which is evaluated using the measurement results of the d remaining projectors. The state with the highest likelihood is the estimate of the unknown state. The method estimates all pure states but a null-measure set. The viability of the protocol is experimentally demonstrated using two different and complementary high-dimensional quantum information platforms. First, by exploring the photonic path-encoding strategy, we validate the method on a single 8-dimensional quantum system. Then, we resort to the five superconducting qubit IBM quantum processor to demonstrate the high performance of the method in the multipartite scenario.

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Section: Accuracy Of the 3bb-qt Methodsmentioning

confidence: 99%

Estimation of pure states using three measurement bases

Zambrano

Pereira

Martínez

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The method here proposed reaches the quantum accuracy limit after a small number of iterations, typically of the order of 8, for all inspected dimensions. Thereby, the method makes an optimal use of the ensemble size and surpasses the estimation accuracy of known methods for pure-state tomography 32 – 35 . Moreover, the method also surpasses the estimation accuracy of any tomographic method designed to estimate mixed states via separable measurements on the ensemble of equally prepared copies.…”

Section: Introductionmentioning

confidence: 99%

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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“…The method here proposed reaches the quantum accuracy limit after a small number of iterations, typically of the order of 8, for all inspected dimensions. Thereby, the method makes an optimal use of the ensemble size and surpasses the estimation accuracy of known methods for pure-state tomography [32][33][34][35] . Moreover, the method also surpasses the estimation accuracy of any tomographic method designed to estimate mixed states via separable measurements on the ensemble of equally prepared copies.…”

Section: Introductionmentioning

confidence: 99%

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

Preprint

View full text Add to dashboard Cite

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.

show abstract

Improved estimation accuracy of the 5-bases-based tomographic method

Cited by 12 publications

References 44 publications

Estimation of pure states using three measurement bases

Estimation of pure states using three measurement bases

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

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

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