“Super-Heisenberg” and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field

Hou, Zhibo; Yan, Jin; Chen, Hongzhen; Tang, Jun-Feng; Huang, Changjiang; Yuan, Haidong; Xiang, Guo-Yong; Li, Chuan‐Feng; Guo, Guang‐Can

doi:10.1103/physrevlett.126.070503

Cited by 39 publications

(16 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In quantum metrology counter-diabatic-like techniques have already been applied to the estimation of parameters in time-dependent Hamiltonians by forcing the time-evolved state to maximize the quantum Fisher information at every point in time [37][38][39]. However, here we consider the case where the part of the Hamiltonian that depends on the unknown parameter is time-independent.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

Gietka

Metz

Keller

et al. 2021

Quantum

View full text Add to dashboard Cite

We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

show abstract

Section: Introductionmentioning

confidence: 99%

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

Gietka

Metz

Keller

et al. 2021

Quantum

View full text Add to dashboard Cite

show abstract

“…For frequency estimation with a single-mode field, the Heisenberg limit becomes ∆λ = 8t 2 ( n 2 + n ) [21] ( n being the average number of photons) and is saturated using a squeezed vacuum state. If the imprinting mechanism Ĥλ is additionally time-dependent, optimal control techniques can be used to maximize the quantum Fisher information by changing x in time such that the instantaneous state becomes the superposition of maximal and minimal eigenvalue eigenstate of the local generator [22,23]. However, the Hamiltonian might then be a complicated function of time as it is no longer composed of only Ĥλ but also involves Ĥ(x) which in general does not commute with Ĥλ .…”

Section: Introductionmentioning

confidence: 99%

Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

Gietka,

Ruks,

Busch

2021

Preprint

View full text Add to dashboard Cite

We present a quantum metrology protocol which relies on quenching a light-matter system exhibiting a superradiant quantum phase transition beyond its critical point. In the thermodynamic limit these systems can exhibit an exponential divergence of the quantum Fisher information in time, whose origin is the exponential growth of the number of correlated photons on an arbitrarily fast time scale determined by the coupling strength. This provides an exponential speed-up in the growth of the quantum Fisher information over existing critical quantum metrology protocols observing power law behaviour. We demonstrate that the Cramér-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage in the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms N in the cavity, despite existing works suggesting a requirement of N -body coupling terms.

show abstract

“…The Hamiltonian discussed in this paper is time independent, if it is time dependent, for instance estimating the magnitude and the frequency of a rotating magnetic field given by Ĥ(x) = −2B n ξ • J with n ξ = (cos(ωt), 0, sin(ωt)), the form of quantum control needs to be correspondingly altered [24,39]. In addition, in the experiment, the employed X c (Eq.…”

Section: Discussionmentioning

confidence: 99%

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

Yang,

Ru,

et al. 2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

“Super-Heisenberg” and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field

Cited by 39 publications

References 60 publications

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

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

Contact Info

Product

Resources

About