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

Gietka, Karol; Metz, Friederike; Keller, Tim; Li, Jing

doi:10.22331/q-2021-07-01-489

Cited by 27 publications

(18 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…What is more, we can now use the condition from equation (24), to find the approximate ground state at the critical point. We know that at the critical point the number of excitations is…”

Section: Lipkin-meshkov-glick Modelmentioning

confidence: 99%

“…This happens because reaching the Heisenberg limit requires having the optimal state from the beginning of the protocol. As the starting state of the critical metrology protocols is uncorrelated, critical metrology cannot reach the Heisenberg limit [24]. What is more, such protocols might last for a very long time since they are focused on approaching the critical points where the gap closes.…”

Section: Quantum Metrologymentioning

confidence: 99%

“…In the above expression, |ψ is the initial state that does not depend on the unknown parameter, and ĥ = i Û † ∂ ω Û with Û being the time evolution operator. According to the above expression, critical metrology protocols cannot reach the Heisenberg limit [24] as the instantaneous eigen state |ψ cannot be the same as the optimal state |φ . This however should not be seen as a major drawback as the derivation of the Heisenberg limit assumes instantaneous generation of an optimal state.…”

Section: Quantum Fisher Informationmentioning

confidence: 99%

See 2 more Smart Citations

Squeezing by Critical Speeding-up: Applications in Quantum Metrology

Gietka

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We present an alternative protocol allowing for the preparation of critical states that instead of suffering from the critical slowing-down benefits from the critical speeding-up. Paradoxically, we prepare these states by going away from the critical point which allows for the speedup. We apply the protocol to the paradigmatic quantum Rabi model and its classical oscillator limit as well as the Lipkin-Meshkov-Glick model. Subsequently, we discuss the application of the adiabatic speed-up protocol in quantum metrology and compare its performance with critical quantum metrology. We show that critical quantum metrology with the Lipkin-Meshkov-Glick model cannot even overcome the standard quantum limit, and we argue that, in general, critical metrology is a suboptimal metrological strategy. Finally, we conclude that systems exhibiting a phase transition are indeed interesting from the viewpoint of quantum technologies, however, it may not be the critical point that should attract the most attention.

show abstract

“…What is more, we can now use the condition from equation (24), to find the approximate ground state at the critical point. We know that at the critical point the number of excitations is…”

Section: Lipkin-meshkov-glick Modelmentioning

confidence: 99%

Section: Quantum Metrologymentioning

confidence: 99%

Section: Quantum Fisher Informationmentioning

confidence: 99%

See 1 more Smart Citation

Squeezing by Critical Speeding-up: Applications in Quantum Metrology

Gietka

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In these systems, we have only a finite numbers of components interacting; the usual thermodynamic limit is then replaced by a scaling of the system parameters [31][32][33][34][35]. A variety of protocols based on finite-component QPTs have been proposed considering light-matter interaction models [36][37][38][39][40][41] and quantum nonlinear resonators [42]. A critical quantum sensor can then be realized using small-scale atomic or solid-state devices, circumventing the complexity of implementing and controlling many-body quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Critical quantum metrology with fully-connected models: from Heisenberg to Kibble–Zurek scaling

Garbe

Abah

Felicetti

et al. 2022

Quantum Sci. Technol.

View full text Add to dashboard Cite

Phase transitions represent a compelling tool for classical and quantum sensing applications. It has been demonstrated that quantum sensors can in principle saturate the Heisenberg scaling, the ultimate precision bound allowed by quantum mechanics, in the limit of large probe number and long measurement time. Due to the critical slowing down, the protocol duration time is of utmost relevance in critical quantum metrology. However, how the long-time limit is reached remains in general an open question. So far, only two dichotomic approaches have been considered, based on either static or dynamical properties of critical quantum systems. Here, we provide a comprehensive analysis of the scaling of the quantum Fisher information for diﬀerent families of protocols that create a continuous connection between static and dynamical approaches. In particular, we consider fully-connected models, a broad class of quantum critical systems of high experimental relevance. Our analysis unveils the existence of universal precision-scaling regimes. These regimes remain valid even for ﬁnite-time protocols and ﬁnite-size systems. We also frame these results in a general theoretical perspective, by deriving a precision bound for arbitrary time-dependent quadratic Hamiltonians.

show abstract

“…Beyond their fundamental interest, finite-component phase transitions open perspectives for quantum technologies. Notably, finite-component critical phenomena in atomic and solidstate devices are promising candidates for the development of critical quantum sensors [42][43][44][45][46][47][48][49][50][51][52][53].…”

mentioning

confidence: 99%