Erratum: Compatibility in multiparameter quantum metrology [Phys. Rev. A 
<b>94</b>
, 052108 (2016)]

Ragy, Sammy; Jarzyna, Marcin; Demkowicz-Dobrzański, RafałÂ

doi:10.1103/physreva.99.029905

Cited by 40 publications

(65 citation statements)

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“…This number will provide a criterion for the construction of estimation processes. Reference [18] evaluates this number in specific cases. In this paper, we consider the multiple parameter estimation and derive an upper bound on the number of such parameters.…”

Section: Introductionmentioning

confidence: 99%

An upper bound on the number of compatible parameters in simultaneous quantum estimation

Kukita¹

2020

J. Phys. A: Math. Theor.

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Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not necessarily achievable. There exists a necessary and sufficient condition for its achievability. It is unknown how many parameters can be estimated while satisfying this condition. In this paper, we analyse an upper bound on the number of such parameters through linear-algebraic techniques. This upper bound depends on the algebraic structure of the quantum system used as a probe. We explicitly calculate this bound for two quantum systems: single qubit and two-qubit X-states.

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Section: Introductionmentioning

confidence: 99%

An upper bound on the number of compatible parameters in simultaneous quantum estimation

Kukita¹

2020

J. Phys. A: Math. Theor.

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“…A sufficient condition for the saturation is indeed [L µ , L ν ] = 0, which is however not a necessary condition. Within the comprehensive framework of quantum local asymptotic normality (QLAN) [59][60][61][62], a necessary and sufficient condition for the saturation of the multi-parameter CRB is given by U µν = 0 for all µ and ν [63].…”

Section: Multi-parameter Incompatibility: a Measure Of Quantumnessmentioning

confidence: 99%

“…This is due to the non-commutativity of measurements associated to independent parameters. It turns out that, within a relatively general setting, known as quantum local asymptotic normality [59][60][61][62], the multi-parameter quantum Cramér-Rao bound (5) is attainable iff [63] U µν = 0, ∀µ, ν,…”

Section: Introductionmentioning

confidence: 99%

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On quantumness in multi-parameter quantum estimation

et al. 2019

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In this article we derive a measure of quantumness in quantum multiparameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér-Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram.

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“…,35,38,39]. The minima are located in the vicinity of B 1 T 1 = (1/2 + k)π and B 2 T 2 = (1 + 2k)π 2 /4, seeFig.…”

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confidence: 94%

Simultaneous Measurement of dc and ac Magnetic Fields at the Heisenberg Limit

2020

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High-precision magnetic field measurement is an ubiquitous issue in physics and a critical task in metrology. Generally, magnetic field has DC and AC components and it is hard to extract both DC and AC components simultaneously. The conventional Ramsey interferometry can easily measure DC magnetic fields, while it becomes invalid for AC magnetic fields since the accumulated phases may average to zero. Here, we propose a scheme for simultaneous measurement of DC and AC magnetic fields by combining Ramsey interferometry and rapid periodic pulses. In our scheme, the interrogation stage is divided into two signal accumulation processes linked by a unitary operation. In the first process, only DC component contributes to the accumulated phase. In the second process, by applying multiple rapid periodic π pulses, only the AC component gives rise to the accumulated phase. By selecting suitable input state and the unitary operations in interrogation and readout stages, and the DC and AC components can be extracted by population measurements. In particular, if the input state is a GHZ state and two interaction-based operations are applied during the interferometry, the measurement precisions of DC and AC magnetic fields can approach the Heisenberg limit simultaneously. Our scheme provides a feasible way to achieve Heisenberglimited simultaneous measurement of DC and AC fields. J m=−J C m J 2 J [(−1) m + 1]|J, m − 1 √ 2 [cos(B 1 JT 1 ) sin(B 2 JT 2 /π) + i sin(B 1 JT 1 ) cos(B 2 JT 2 /π)] J m=−J C m J 2 J [(−1) m − 1]|J, m = 1 √ 2 {cos(B 1 JT 1 )[cos(B 2 JT 2 /π) − sin(B 2 JT 2 /π)] − i sin(B 1 JT 1 )[cos(B 2 JT 2 /π) + sin(B 2 JT 2 /π)]} J m=−J C m J 2 J (−1) m |J, m + 1 √ 2 {cos(B 1 JT 1 )[cos(B 2 JT 2 /π) + sin(B 2 JT 2 /π)] + i sin(B 1 JT 1 )[cos(B 2 JT 2 /π) − sin(B 2 JT 2 /π)]} J m=−J C m J 2 J |J, m .

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Erratum: Compatibility in multiparameter quantum metrology [Phys. Rev. A 94 , 052108 (2016)]

Abstract: Erratum: Compatibility in multiparameter quantum metrology [Phys. Rev. A 94, 052108 (2016)]

Cited by 40 publications

References 0 publications

An upper bound on the number of compatible parameters in simultaneous quantum estimation

An upper bound on the number of compatible parameters in simultaneous quantum estimation

On quantumness in multi-parameter quantum estimation

Simultaneous Measurement of dc and ac Magnetic Fields at the Heisenberg Limit

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