Relating Fisher information to order parameters

Prokopenko, Mikhail; Lizier, Joseph T.; Obst, Oliver; Wang, X. Rosalind

doi:10.1103/physreve.84.041116

Cited by 104 publications

(127 citation statements)

References 29 publications

Supporting

Mentioning

117

Contrasting

Order By: Relevance

“…Since it is this elastic peak that diverges at thermal phase transitions, these do not appear as particular features in F Q . We can connect the elastic peak to the classical contribution to the Fisher information [41]. Equation (S17) yields F C = λ (∂p λ /∂ϑ) 2 p λ = χ el /T .…”

Section: S4 Classical Contribution To Qfi and Behaviour At Thermal Pmentioning

confidence: 99%

See 1 more Smart Citation

Measuring multipartite entanglement through dynamic susceptibilities

et al. 2016

View full text Add to dashboard Cite

Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This moreover establishes a fundamental connection between multipartite entanglement and many-body correlations contained in response functions, with profound implications close to quantum phase transitions. There, the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartiteness of entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments.Entanglement is a central theoretical concept underlying the characterisation of quantum many-body states in condensed-matter and high-energy physics, as well as quantum information. For example, entanglement properties reveal exotic states of matter such as topological spin liquids [1] or many-body localization [2,3], the holographic entanglement entropy identifies confinement/deconfinement transitions in gauge theories [4,5], and entanglement is considered the central resource for quantum-enhanced metrology [6,7] as well as quantum computation [8][9][10][11]. In experiments, entanglement becomes measurable via a tomographic determination of the many-particle quantum state [12][13][14][15], and protocols have been developed [16] and implemented in remarkable experiments [17] to measure entanglement entropies in quench dynamics and quantum phase transitions. However, the resources required by these protocols scale exponentially with the system size, and these experimental efforts are thus limited a priori to few-particle systems.To address the problem of detecting and quantifying multipartite entanglement for large systems, we consider below the quantum Fisher information (QFI) as an entanglement witness [18][19][20]. Our key result is thatfor a many-body system at thermal equilibrium at any temperature-the QFI can be determined directly from a measurement of Kubo linear response functions, in particular the dynamic susceptibility (see Fig. 1). We emphasise that this measurement prescription is independent of microscopic details of the system of interest and that the measurement of linear response is a standard tool in experiments. Importantly, only modest measurement resources are required that do not scale with system size. The presented prescription therefore makes multipartite entanglement observable for a large variety of * philipp.hauke@uibk.ac.at χ (ω, T ) gives the quantum Fisher information (shaded areas). (c) This pro...

show abstract

Section: S4 Classical Contribution To Qfi and Behaviour At Thermal Pmentioning

confidence: 99%

“…It is χ el that diverges at a thermal phase transition. As is shown in the Supplementary Material [30], χ el can be related to the Fisher information in a classical scenario [41] that has no relation to entanglement. The second term χ vV , on the other hand, remains smooth at thermal transitions.…”

mentioning

confidence: 99%

Measuring multipartite entanglement through dynamic susceptibilities

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Their results suggest that theoretically, we can predict critical thresholds in epidemics [14], which could be of a substantial value in health care. In practice, one of the challenges lies in pinpointing such critical thresholds in finite-size systems, where a precise identification of phase transitions requires an estimation of the rate of change of the order parameter, often from finite and/or distributed data [15,16].…”

Section: Introductionmentioning

confidence: 99%

Criticality and Information Dynamics in Epidemiological Models

Erten

Lizier

Piraveenan

et al. 2017

Entropy

Self Cite

View full text Add to dashboard Cite

Abstract:Understanding epidemic dynamics has always been a challenge. As witnessed from the ongoing Zika or the seasonal Influenza epidemics, we still need to improve our analytical methods to better understand and control epidemics. While the emergence of complex sciences in the turn of the millennium have resulted in their implementation in modelling epidemics, there is still a need for improving our understanding of critical dynamics in epidemics. In this study, using agent-based modelling, we simulate a Susceptible-Infected-Susceptible (SIS) epidemic on a homogeneous network. We use transfer entropy and active information storage from information dynamics framework to characterise the critical transition in epidemiological models. Our study shows that both (bias-corrected) transfer entropy and active information storage maximise after the critical threshold (R 0 = 1). This is the first step toward an information dynamics approach to epidemics. Understanding the dynamics around the criticality in epidemiological models can provide us insights about emergent diseases and disease control.

show abstract

“…In recent decade different concepts emerging from quantum-information geometry [1][2][3][4] have been intensively incorporated in condensed matter physics [5][6][7][8][9][10][11][12][13][14][15][16][17]. The underlying idea may be briefly reviewed as follows.…”

Section: Introductionmentioning

confidence: 99%

“…The notion of distance has found applications in different fields. For example: thermodynamic of small systems [5,16], geometrical description of phase transitions and quantum criticality [6][7][8][9][10][11][12][13][14][15], quantum estimation of Hamiltonian parameters [18,19] and hypothesis testing and discrimination of states [20][21][22][23], are only a part of them. If we consider the distance between two states obtained by an infinitesimal change in the values of the parameters that specifie the quantum state, we come to the notion of a metric tensor, i.e.…”

Section: Introductionmentioning

confidence: 99%

Monotone Riemannian metrics and dynamic structure factor in condensed matter physics

Tonchev

2016

Journal of Mathematical Physics

View full text Add to dashboard Cite

An analytical approach is developed to the problem of computation of monotone Riemannian metrics (e.g. Bogoliubov-Kubo-Mori, Bures, Chernoff, etc.) on the set of quantum states. The obtained expressions originate from the Morozova,Cencov and Petz correspondence of monotone metrics to operator monotone functions. The used mathematical technique provides analytical expansions in terms of the thermodynamic mean values of iterated (nested) commutators of a model Hamiltonian T with the operator S involved through the control parameter h. Due to the sum rules for the frequency moments of the dynamic structure factor new presentations for the monotone Riemannian metrics are obtained. Particularly, relations between any monotone Riemannian metric and the usual thermodynamic susceptibility or the variance of the operator S are discussed. If the symmetry properties of the Hamiltonian are given in terms of generators of some Lie algebra, the obtained expansions may be evaluated in a closed form. These issues are tested on a class of model systems studied in condensed matter physics.2

show abstract

Relating Fisher information to order parameters

Cited by 104 publications

References 29 publications

Measuring multipartite entanglement through dynamic susceptibilities

Measuring multipartite entanglement through dynamic susceptibilities

Criticality and Information Dynamics in Epidemiological Models

Monotone Riemannian metrics and dynamic structure factor in condensed matter physics

Contact Info

Product

Resources

About