Optimally controlled quantum discrimination and estimation

Basilewitsch, Daniel; Yuan, Haidong; Koch, Christiane P.

doi:10.1103/physrevresearch.2.033396

Cited by 28 publications

(43 citation statements)

References 72 publications

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“…Then how to make the temporary control converges to the optimal form as fast as possible, is the subsequent problem. Some algorithm such as the gradient ascent pulse engineering (GRAPE) [41], the Krotov algorithm [42,43], the chopped random-basis (CRAB) method [44], and some related variants [45][46][47] offer many possibilities for the solution. The pertinent discussions belong to quantum optimal control theory [48], which will be the focus of our next work.…”

Section: Discussionmentioning

confidence: 99%

Multiparameter simultaneous optimal estimation with an SU(2) coding unitary evolution

Yang,

Ru,

et al. 2022

Preprint

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In a ubiquitous SU (2) dynamics, achieving the simultaneous optimal estimation of multiple parameters is significant but difficult. Using quantum control to optimize this SU (2) coding unitary evolution is one of solutions. We propose a method, characterized by the nested cross-products of the coefficient vector X of SU (2) generators and its partial derivative ∂ X, to investigate the control-enhanced quantum multiparameter estimation. Our work reveals that quantum control is not always functional in improving the estimation precision, which depends on the characterization of an SU (2) dynamics with respect to the objective parameter. This characterization is quantified by the angle α between X and ∂ X. For an SU (2) dynamics featured by α = π/2, the promotion of the estimation precision can get the most benefits from the controls. When α gradually closes to 0 or π, the precision promotion contributed to by quantum control correspondingly becomes inconspicuous. Until a dynamics with α = 0 or π, quantum control completely loses its advantage. In addition, we find a set of conditions restricting the simultaneous optimal estimation of all the parameters, but fortunately, which can be removed by using a maximally entangled two-qubit state as the probe state and adding an ancillary channel into the configuration. Lastly, a spin-1/2 system is taken as an example to verify the above-mentioned conclusions. Our proposal sufficiently exhibits the hallmark of control-enhancement in fulfilling the multiparameter estimation mission, and it is applicable to an arbitrary SU (2) parametrization process.

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Section: Discussionmentioning

confidence: 99%

Multiparameter simultaneous optimal estimation with an SU(2) coding unitary evolution

Yang,

Ru,

et al. 2022

Preprint

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“…The search of optimal probe states is thus an essential step in the design of optimal schemes. Various methodologies, including direct analytical calculations [84][85][86][87][88][89][90][91][92][93][94], semianalytical [95][96][97][98][99][100] and full numerical approaches [101][102][103][104][105], have been proposed and discussed. More advances of the state optimization in quantum metrology can be found in a recent review [17].…”

Section: State Optimizationmentioning

confidence: 99%

QuanEstimation: an open-source toolkit for quantum parameter estimation

Zhang¹,

Yu²,

Yuan³

et al. 2022

Preprint

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Quantum parameter estimation promises a high-precision measurement in theory, however, how to design the optimal scheme in a specific scenario, especially under a practical condition, is still a serious problem that needs to be solved case by case due to the existence of multiple mathematical bounds and optimization methods. Depending on the scenario considered, different bounds may be more or less suitable, both in terms of computational complexity and the tightness of the bound itself. At the same time, the metrological schemes provided by different optimization methods need to be tested against realization complexity, robustness, etc. Hence, a comprehensive toolkit containing various bounds and optimization methods is essential for the scheme design in quantum metrology. To fill this vacancy, here we present a Python-Julia-based open-source toolkit for quantum parameter estimation, which includes many well-used mathematical bounds and optimization methods. Utilizing this toolkit, all procedures in the scheme design, such as the optimizations of the probe state, control and measurement, can be readily and efficiently performed.

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“…[39,120,129], and the codes have been integrated into the package QuanEstimation. Besides GRAPE, Krotov's method has also been employed in the design of optimal control in quantum metrology [130].…”

Section: A Quantum Controlmentioning

confidence: 99%

Optimal Scheme for Quantum Metrology

Liu,

Zhang,

Chen

et al. 2021

Preprint

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Quantum metrology can achieve far better precision than classical metrology, and is one of the most important applications of quantum technologies in the real world. To attain the highest precision promised by quantum metrology, all steps of the schemes need to be optimized, which include the state preparation, parametrization and measurement. Here we review the recent progresses on the optimization of these steps, which are essential for the identification and achievement of the ultimate precision limit in quantum metrology. We hope this provides a useful reference for the researchers in quantum metrology and related fields.

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Optimally controlled quantum discrimination and estimation

Cited by 28 publications

References 72 publications

Multiparameter simultaneous optimal estimation with an SU(2) coding unitary evolution

Multiparameter simultaneous optimal estimation with an SU(2) coding unitary evolution

QuanEstimation: an open-source toolkit for quantum parameter estimation

Optimal Scheme for Quantum Metrology

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