Maximal quantum Fisher information for general su(2) parametrization processes

Jing, Xiao-Xing; Liu, Jing; Xiong, Heng-Na; Wang, Xiaoguang

doi:10.1103/physreva.92.012312

Cited by 34 publications

(31 citation statements)

References 56 publications

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“…A more general case is that the Hamiltonian is still independent of time but the parameter to estimate is not necessarily multiplicative. This has attracted a lot of attention recently 46 47 48 50 51 52 67 . The Hamiltonian in this case can be represented as H g ( t )= H g in general.…”

Section: Resultsmentioning

confidence: 99%

“…While most previous research on quantum metrology was focused on multiplicative parameters of Hamiltonians, growing attention has recently been drawn to more general parameters of Hamiltonians 46 or physical dynamics 47 48 , such as those of magnetic fields 46 49 50 51 . Interestingly, in contrast to estimation of multiplicative parameters, estimation of general Hamiltonian parameters exhibits distinct characteristics in some aspects, particularly in the time scaling of the Fisher information 46 , and often requires quantum control to gain the highest sensitivity 52 .…”

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confidence: 99%

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Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

2017

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Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

2017

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“…In the latter part of this paper, we explicitly calculate this upper bound for two examples: single-qubit states and two-qubit X-states. These states appear in many applications of quantum information theory [4,29,[36][37][38][39]. This paper is organised as follows.…”

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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“…where n θ = (− cos Bt sin θ, − sin Bt, cos Bt cos θ). The maximal QFI is then J θ Q = 4 sin 2 (Bt) [55,57]. Similarly the optimal state can be taken as |ψ(0) = |λmax +|λmin √ 2…”

Section: Precision Under the Unitary Dynamicsmentioning

confidence: 99%

Fluctuation-enhanced quantum metrology

Chen,

Liu

et al. 2020

Preprint

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The main obstacle for practical quantum technology is the noise, which can induce the decoherence and destroy the potential quantum advantages. The fluctuation of a field, which induces the dephasing on the system, is one of the most common noises and widely regarded as detrimental to quantum technologies. Here we show, contrary to the conventional belief, the fluctuation can be used to improve the precision limits in quantum metrology for the estimation of various parameters. Specifically, we show that for the estimation of the direction and rotating frequency of a field, the achieved precisions at the presence of the fluctuation can even surpass the highest precision achievable under the unitary dynamics which have been widely taken as the ultimate limit. We provide explicit protocols, which employs the adaptive quantum error correction, to achieve the higher precision limits with the fluctuating fields. Our study provides a completely new perspective on the role of the noises in quantum metrology. It also opens the door for higher precisions beyond the limit that has been believed to be ultimate.

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Maximal quantum Fisher information for general su(2) parametrization processes

Cited by 34 publications

References 56 publications

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

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

Fluctuation-enhanced quantum metrology

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