Achieving sub-shot-noise sensing at finite temperatures

Mehboudi, Mohammad; Correa, Luis Alfonso; Sanpera, Anna

doi:10.1103/physreva.94.042121

Cited by 30 publications

(41 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The quantity F (β,ˆ P ) was tagged 'local quantum thermal susceptibility' in reference [34]. This was shown to display the same qualitative behaviour as the global energy variance around quantum phase crossovers in locally interacting spin chains at finite temperatures [99,44,104]. Indeed one can rigorously prove that the relative error made when approximating F (β,ˆ P ) by (∆Ĥ P ) 2 -i.e., | F (β,ˆ P ) − ∆Ĥ P |/∆Ĥ P -decreases as the 'volume-to-surface' ratio of P grows [153].…”

Section: Local Temperature Fluctuationsmentioning

confidence: 99%

Thermometry in the quantum regime: recent theoretical progress

Mehboudi¹,

Sanpera²,

Correa³

2019

J. Phys. A: Math. Theor.

Self Cite

153

176

View full text Add to dashboard Cite

Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out of thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.

show abstract

Section: Local Temperature Fluctuationsmentioning

confidence: 99%

Thermometry in the quantum regime: recent theoretical progress

Mehboudi¹,

Sanpera²,

Correa³

2019

J. Phys. A: Math. Theor.

Self Cite

153

176

View full text Add to dashboard Cite

show abstract

“…Having all the above in mind, one immediately recalls the second approach that connects the estimation problem to the concept of criticality [37][38][39][40][41][42][43][44][45]. In that approach one focuses on the situation where the dependence of the state on λ has a completely different origin.…”

Section: Introductionmentioning

confidence: 99%

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

et al. 2018

View full text Add to dashboard Cite

We address the question of whether the super-Heisenberg scaling for quantum estimation is indeed realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter-dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian, the precision of its estimation is known to scale at most as N −1 (Heisenberg scaling) in terms of the number of elementary subsystems used N. The second approach compares the overlap between the ground states of the parameter-dependent Hamiltonian in critical systems, often leading to an apparent super-Heisenberg scaling. However, we point out that if one takes into account the scaling of time needed to perform the necessary operations, i.e., ensuring adiabaticity of the evolution, the Heisenberg limit given by the rotation scenario is recovered. We illustrate the general theory on a ferromagnetic Heisenberg spin chain example and show that it exhibits such super-Heisenberg scaling of ground-state fidelity around the critical value of the parameter (magnetic field) governing the one-body part of the Hamiltonian. Even an elementary estimator represented by a single-site magnetization already outperforms the Heisenberg behavior providing the N −1.5 scaling. In this case, Fisher information sets the ultimate scaling as N −1.75 , which can be saturated by measuring magnetization on all sites simultaneously. We discuss universal scaling predictions of the estimation precision offered by such observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We provide an experimental proposal of realization of the considered model via mapping the system to ultracold bosons in a periodically shaken optical lattice. We explicitly derive that the Heisenberg limit is recovered when the time needed for preparation of quantum states involved is taken into account.

show abstract

“…For sufficiently small λ, in a finite system, one hasFidelity susceptibility is directly related to the quantum Fisher information (QFI), G, being directly proportional to the Bures distance between density matrices at slightly differing values of λ [26,27], with G(λ) = 4χ. Fidelity susceptibility emerged as a useful tool to study quantum phase transitions as at the transition point the ground state changes rapidly leading to the enhancement of χ [27][28][29][30][31][32][33][34]. All of these studies were restricted to ground state properties while MBL considers the bulk of excited states (for a discussion of thermal states see [35][36][37][38]).…”

mentioning

confidence: 99%

Fidelity susceptibility in Gaussian random ensembles

et al. 2019

View full text Add to dashboard Cite

The fidelity susceptibility measures sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here we propose to use the fidelity susceptibility as a useful dimensionless measure for complex quantum systems. We find analytically the fidelity susceptibility distributions for Gaussian orthogonal and unitary universality classes for arbitrary system size. The results are verified by a comparison with numerical data.The discovery of many body localization (MBL) phenomenon resulting in non-ergodicity of the dynamics in many body systems [1] restored also the interest in purely ergodic phenomena modeled by Gaussian random ensembles (GRE) [2] and in possible measures to characterize them. The gap ratio between adjacent level spacings [3] was introduced precisely for that purpose as it does not involve the so called unfolding [4] necessary for meaningful studies of level spacing distributions and yet often leading to spurious results [5]. Still, the level spacing distribution belongs to the most popular statistical measures used for single particle quantum chaos studies [6][7][8][9] and also in the transition to MBL [10-13]. A particular place among different measures was taken by those characterizing level dynamics for a Hamiltonian H(λ) dependent on some parameter λ. In Pechukas-Yukawa formulation [14,15] energy levels are positions of a fictitious gas particles, derivatives with respect to the fictitious time λ are velocities (level slopes), the second derivatives describe curvatures of the levels (accelerations). Simons and Altschuler [16] put forward a proposition that the variance of velocities distribution is an important parameter characterizing universality of level dynamics. This led to predictions for distributions of avoided crossings [17] and, importantly, curvature distributions postulated first on the basis of numerical data for GRE [18] and then derived analytically via supersymmetric method by von Oppen [19,20] (for alternative techniques see [21,22]). Curvature distributions were recently addressed in MBL studies [23,24].Apart from quantum chaos studies in the eighties and nineties of the last millennium, another "level dynamics" tool has been introduced in the quantum information area, i.e. the fidelity [25]. It compares two close (possibly mixed) quantum states. If these states are dependent on a parameter λ it is customary to introduce a fidelity susceptibility χ. For sufficiently small λ, in a finite system, one hasFidelity susceptibility is directly related to the quantum Fisher information (QFI), G, being directly proportional to the Bures distance between density matrices at slightly differing values of λ [26,27], with G(λ) = 4χ. Fidelity susceptibility emerged as a useful tool to study quantum phase transitions as at the transition point the ground state changes rapidly leading to the enhancement of χ [27][28][29][30][31][32][33][34]. All of these studies w...

show abstract

Achieving sub-shot-noise sensing at finite temperatures

Cited by 30 publications

References 62 publications

Thermometry in the quantum regime: recent theoretical progress

Thermometry in the quantum regime: recent theoretical progress

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

Fidelity susceptibility in Gaussian random ensembles

Contact Info

Product

Resources

About