Bandt-Pompe approach to the classical-quantum transition

By regarding the celebrated classical-quantum transition problem as one pertaining to the domain of dynamic systems’ theory, we present a discussion that exhibits the superiority of the Bandt-Pompe approach to the extraction of a probability distribution from time series’ values.     

The Tsallis-complexity of a semiclassical time-evolution

An investigation is undertaken of semiclassical time-evolutions and their classical limit with the intent of getting insights into the classical–quantum frontier. We deal with a system that represents the interaction between matter and a given field, and our main research tool is the so-called q$q$-complexity quantifier, for which two different versions are considered. The probability distribution associated with the time-evolution process is determined by recourse to the Bandt–Pompe symbolic technique [C. Bandt, B. Pompe, Permutation entropy: a natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102:1–174102:4]. The most salient details of the quantum–classical transition turn out to be described not only well, but also in a better fashion than that of previous literature.     

Fisher information,Rényi entropy power and quantum phase transition in the Dicke model

Fisher information, Rényi entropy power and Fisher–Rényi information product are presented for the Dicke model. There is a quantum phase transition in this quantum optical model. It is pointed out that there is an abrupt change in the Fisher information, Rényi entropy power, the Fisher, Shannon and Rényi lengths at the transition point. It is found that these quantities diverge as the characteristic length: |_λc−λ|^−1/4${|{\lambda }_c-\lambda |}^{-1/4}$ around the critical value of the coupling strength _λc${\lambda }_c$ for any value of the parameter β$\beta$.     

Chaos and quantum Fisher information in the quantum kicked top

Quantum Fisher information is related to the problem of parameter estimation.Recently,a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information.This paper studies the behaviours of quantum Fisher information in the quantum kicked top model,whose classical correspondence can be chaotic.It finds that,first,detected by quantum Fisher information,the quantum kicked top is entangled whether the system is in chaotic or in regular case.Secondly,the quantum Fisher information is larger in chaotic case than that in regular case,which means,the system is more sensitive in the chaotic case.     

Fisher information due to a phase noisy laser under non-Markovian environment

More recently, K. Berrada [Annals of Physics 340 (2014) 60-69] [1] studied the geometric phase of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system, and collapse and revival phenomena were found for large class of states. In this paper, using this noise effect, we study the quantum fisher information (QFI) for a two-level atom system driven by a phase noise laser under non-Markovian dynamics. A new quantity, called QFI flow is used to characterize the damping effect and unveil a fundamental connection between non-Markovian behavior and dynamics of system–environment correlations under phase noise laser. It is shown that QFI flow has disappeared suddenly followed by a sudden birth depending on the kind of the environment damping. QFI flow provides an indicator to characterize the dissipative quantum system’s decoherence by analyzing the behavior of the dynamical non-Markovian coefficients.     

玻色-爱因斯坦凝聚系统的量子Fisher信息与混沌

量子Fisher信息作为经典Fisher信息的自然推广,与量子信息中的纠缠判断具有密切联系.在表现为典型量子混沌特征的受击两分量玻色-爱因斯坦凝聚系统中,研究了与经典相空间对应的纠缠和量子Fisher信息动力学性质. 结果表明,初次撞击后的系统量子态是纠缠的,与初态所处相空间中的混乱程度无关.而量子Fisher信息的动力学演化对系统初态非常敏感,当初态处于混沌区域时,量子Fisher信息值比初态处于规则区域时大.利用这种较好的量子-经典对应关系,得到量子Fisher信息可以刻画量子混沌的结论. 关键词： 量子Fisher信息 玻色-爱因斯坦凝聚 量子混沌 量子-经典对应     

Semiclassical information from deformed and escort information measures

Escort distributions are a well established but (for physicists) a relatively new concept that is rapidly gaining wide acceptance in world. In this work we wish to revisit the concept within the strictures of the celebrated semiclassical Husimi distributions (HDs) and thereby investigate the possibility of extracting new semiclassical information contained, not in the HD themselves, but in their associated escort Husimi distributions. We will also establish relations, for various information measures, between their deformed versions [J. Naudts, Physica A 316 (2002) 323] and those built up with escort HDs. Bounds on the concomitant power exponents will be determined.     

光与物质相互作用系统中的量子Fisher信息和自旋压缩

Fisher信息是估计理论中的重要概念,最近发现与量子信息中的纠缠判据具有密切联系.非旋波近似条件下,Dicke模型经典相空间表现为混沌动力学特征.本文详细考察了Dicke模型描述的光与物质相互作用系统中量子Fisher信息和自旋压缩动力学特性.结果表明:在短时瞬态情况下,无论初态处于规则区域还是混沌区域系统均表现为纠缠性质;但在长时稳态情况下,初态处于规则区域时系统纠缠消失,而初态处于混沌区域时系统则一直存在纠缠.通过与系统自旋压缩动力学性质相比较,发现量子Fisher信息可以更有效地刻画量子混沌.进一步考察初态处于规则和混沌区域时系统密度矩阵和纯度的动力学演化特性,发现混沌导致系统退相干现象发生,说明量子Fisher信息对混沌更敏感.     

Onicescu information energy in terms of Shannon entropy and Fisher information densities

Following recent studies concerning the use of information theory in electronic structure theory of atomic and molecular systems, an analytical relationship between Onicescu information energy and densities of Shannon entropy and the two forms of the Fisher information has been presented. The established proof must be viewed in the light of the exponentially decaying nature of the asymptotic density of atoms and molecules.     

Information and complexity measures in the interface of a metal and a superconductor

Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\mathrm{\Psi }(\mathbf{r})$ derived from the Ginzburg–Landau theory is used as an input together with experimental values of critical transition temperature $T_c$ and the superconducting coherence length ${\xi }_0$. Analytical expressions are obtained for information and complexity measures. Thus $T_c$ is directly related in a simple way with disorder and complexity. An analytical relation is found of the Fisher Information with the energy profile of superconductivity i.e. the ratio of surface free energy and the bulk free energy. We verify that a simple relation holds between Shannon and Fisher information i.e. a decomposition of a global information quantity (Shannon) in terms of two local ones (Fisher information), previously derived and verified for atoms and molecules by Liu et al. Finally, we find analytical expressions for generalized information measures like the Tsallis entropy and Fisher information. We conclude that the proper value of the non-extensivity parameter $q?1$, in agreement with previous work using a different model, where $q?1.005$.     

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system (Kim et al. (2018) [28]). This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.     

Phase damping destroys quantum Fisher information of W states

We study the quantum Fisher information (QFI) of W states in the basic decoherence channels. We show that, as decoherence starts and increases, under i) depolarizing, QFI smoothly decays; ii) amplitude damping, QFI first exhibits a sudden drop to the shot noise level, then decreases to zero and finally increases back to the shot noise level; iii) phase damping, QFI is zero for all non-zero decoherence. We also find that on the contrary to GHZ states, QFI of W states in x and y directions are equal to each other and zero in z direction.     

Propagation of arbitrary initial wave packets in a quantum parametric oscillator: Instability zones for higher order moments

We consider the dynamics of a particle in a parametric oscillator with a view to exploring any quantum feature of the initial wave packet that shows divergent (in time) behaviour for parameter values where the classical motion dynamics of the mean position is bounded. We use Ehrenfest's theorem to explore the dynamics of nth order moment which reduces exactly to a linear non autonomous differential equation of order $n+1$. It is found that while the width and skewness of the packet is unbounded exactly in the zones where the classical motion is unbounded, the kurtosis of an initially non-gaussian wave packet can become infinitely large in certain additional zones. This implies that the shape of the wave packet can change drastically with time in these zones.     

Fisher information for endohedrally confined hydrogen atom

Electron localization and delocalization of endohedrally confined hydrogen atom has been investigated employing Fisher information theory. Confinement has been modeled using a spherical Gaussian-type potential. B-spline bases expansion method was used to solve the Schrödinger equation to obtain the required energy eigenvalues and the corresponding wave functions. Changes in energies with depths of potential are explained using Hellmann-Feynman theorem. The behavior of Fisher information against the confining potential depths and positions are demonstrated. Moreover, our results show that Fisher information is an effective way to measure the localization of valence electrons.     

Geometric phase,entanglement, and quantum Fisher information near the saturation point

Considering a collection of two-level atoms in the presence of a saturating monochromatic, steady-state field, we investigate the geometric phase (GP) of an arbitrary medium’s atom. We find that it is possible to detect the saturation of the atomic response by the GP computation. This is an interesting result, because we can predict the collective behaviour of the atomic system—i.e., the saturation of the optical response of the medium- by investigating the GP of a single medium’s atom, described as a qubit. Moreover, we find that the plot of the atomic GP in terms of the detuning Δ$\Delta$ is very similar to the absorption spectrum of the medium. In addition, it is shown that when the intensity of the driving laser field tends to saturation intensity, the qubit approaches maximum correlation with its environment described by the driving field and other qubits in the atomic system. Furthermore, we find that the behaviour of the entanglement is very analogous to that of the GP and the absorption coefficient. Besides, we adopt the atom to estimate the decoherence parameter by using the quantum Fisher information (QFI), an important measure of the information content of quantum states. Interestingly, we find that when the atomic system approaches its saturation point, the QFI decays with increasing the laser intensity, and therefore the parameter estimation becomes more inaccurate.     

Quantum Fisher information of the GHZ state due to classical phase noise lasers under non-Markovian environment

The dynamics of N$N$-qubit GHZ state quantum Fisher information (QFI) under phase noise lasers (PNLs) driving is investigated in terms of non-Markovian master equation. We first investigate the non-Markovian dynamics of the QFI of N$N$-qubit GHZ state and show that when the ratio of the PNL rate and the system–environment coupling strength is very small, the oscillations of the QFIs decay slower which corresponds to the non-Markovian region; yet when it becomes large, the QFIs monotonously decay which corresponds to the Markovian region. When the atom number N$N$ increases, QFIs in both regions decay faster. We further find that the QFI flow disappears suddenly followed by a sudden birth depending on the ratio of the PNL rate and the system–environment coupling strength and the atom number N$N$, which unveil a fundamental connection between the non-Markovian behaviors and the parameters of system–environment couplings. We discuss two optimal positive operator-valued measures (POVMs) for two different strategies of our model and find the condition of the optimal measurement. At last, we consider the QFI of two atoms with qubit–qubit interaction under random telegraph noises (RTNs).     

Subjective modelling of supply and demand—the minimum of Fisher information solution

Two of the present authors have put forward a projective geometry based model of rational trading that implies a model for subjective demand/supply profiles if one considers closing of a position as a random process. We would like to present the analysis of a subjectivity in such trading models. In our model, the trader gets the maximal profit intensity when the probability of transaction is ∼0.5853. We also present a comparison with the model based on the Maximum of Entropy Principle. To the best of our knowledge, this is one of the first analyses that show a concrete situation in which trader profit optimal value is in the class of price-negotiating algorithms (strategies) resulting in non-monotonic demand (supply) curves of the Rest of the World (a collective opponent). Our model suggests that there might be a new class of rational trader strategies that (almost) neglects the supply-demand profile of the market. This class emerges when one tries to minimize the information that strategies reveal.