Search Results (15)

In this work, we investigate the spectral, information-theoretic, and thermodynamic properties of a fractal Schrödinger system with position-dependent mass subject to an effective semiconductor-like confinement. We employ a fractal momentum operator and a Von Roos Hamiltonian with BenDaniel–Duke ordering to obtain exact analytical solutions for the energy spectrum and wave functions. The interplay between the fractal parameter $\alpha$, the effective lattice scale $l_0$, and the harmonic confinement strength $\omega$ is explored. We perform a comprehensive analysis of the Shannon entropy, Fisher information, and Fisher–Shannon complexity in both coordinate and momentum spaces. Our results demonstrate that these parameters directly control the localization–delocalization transition and the informational architecture of the quantum states, while satisfying the entropic and Fisher uncertainty relations. Furthermore, we derive the exact partition function and the corresponding thermodynamic properties (free energy, internal energy, entropy, and specific heat) of the system. The analytical framework presented offers valuable insights into the spectral, information-theoretic, and thermodynamic behavior of quantum systems in fractal semiconductor-like environments. Full article

We develop an information-geometric framework for describing quantum state-update processes associated with measurement and statistical distinguishability. The approach is based on the quantum relative entropy and the quantum Fisher information metric, which together induce a natural Riemannian geometry on the manifold of quantum states. Using the second-order expansion of relative entropy, we show how the Fisher metric governs the local structure of distinguishability between nearby states and defines a corresponding thermodynamic length. This geometric structure provides an effective description of finite quantum state transitions in terms of fluctuation geometry and information-space distance. The formalism is applied to thermal two-level systems and harmonic oscillator states, illustrating how the Fisher metric encodes susceptibilities, fluctuations, and geometric transition costs. We also discuss the relation between thermodynamic length, dissipation bounds, and optimal paths in state space. Within this framework, wave function collapse is interpreted not as a microscopic dynamical mechanism, but as an effective state-update process that admits a geometric characterization in the manifold of density operators. The resulting perspective unifies concepts from quantum information theory, thermodynamics, and differential geometry within a common operational framework based on statistical distinguishability. Possible connections with quantum speed limits, entanglement geometry, and holographic relations between relative entropy and gravitational dynamics are briefly discussed. Full article

Area-law entropy appears in local quantum ground states, low-temperature Gibbs states, and gravitational physics, whereas classical thermodynamics is formulated with volume-extensive entropy. We propose a coarse-grained information-theoretic framework, based on an effective free-energy functional combining Fisher information, a potential term, and Shannon entropy, that organises these different scalings within a single thermodynamic picture. Comparing localisation costs, external stabilisation, and gravitational self-interaction at the level of scaling reveals three regimes. At microscopic scales, locality and low-temperature coherence enforce area-type entropy scaling. At intermediate scales, volume-law entropy emerges as an effective regime sustained by non-gravitational confinement or external support; in the absence of such support, volume-extensive entropy does not by itself define an intrinsically stable equilibrium. At large scales dominated by gravitational self-interaction, a reduced scaling analysis identifies area-type behaviour as the distinguished infrared scaling, consistent with black-hole thermodynamics and with macroscopic universality requirements. The framework clarifies the limited domain of classical extensivity and offers a unified coarse-grained perspective on the recurrence of area-law scaling across quantum and gravitational settings. Full article

We present a useful method to enhance parameter estimation precision (PEP) in quantum systems by mitigating the detrimental effects of decoherence and environmental noise. We consider a theoretical model featuring a single qubit coupled to a zero-temperature bosonic reservoir with a Lorentzian spectral density, augmented by non-interacting auxiliary qubits. Our analysis spans both Markovian and non-Markovian dynamical regimes, demonstrating that auxiliary qubits effectively preserve PEP by stabilizing quantum Fisher information (QFI) and local quantum uncertainty (LQU), key metrics for precise PEP and quantum correlation. Additionally, detuning between the qubit and reservoir frequencies serves as a tunable parameter to further reduce decoherence. Employing the Kraus operator formalism, we reveal how these strategies create a decoherence-free subspace, offering a passive and scalable approach to protect quantum measurements. The results highlight significant potential for improving quantum metrology and information processing technologies in noisy environments, providing practical insights for advancing quantum system performance. Full article

Within density functional theory (DFT), where the density is the fundamental variable, quantum phase transitions (QPTs) can be formulated through a Hamiltonian $\widehat{H}={\widehat{H}}_0+{\sum }_i{\xi }_i{\widehat{A}}_i$, such that the control parameters $\left\{{\xi }_i\right\}$ are in bijective correspondence (in the nondegenerate case) with the “densities” $a_i=⟨{\widehat{A}}_i⟩$, and the functional $Q\left(\left\{a_i\right\}\right)$ acts as the Legendre transform of the energy; this structure even permits the use of Rényi entropy (for a given order) as an alternative control parameter, while degeneracy can be handled via a subspace density. On this foundation, information-theoretic measures provide sensitive diagnostics of criticality: fidelity and its susceptibility $\chi$, Fisher information, relative Rényi entropy, and the Kullback–Leibler divergence are locally linked by $R^q\approx q{I}_{KL}\approx 2q\chi {\left(\delta \lambda \right)}^2$, revealing their proportionality in the small-parameter-shift regime. Applied to the Dicke model, numerical analyses show that fidelity exhibits pronounced curvature or divergence near ${\lambda }_c=\sqrt{\omega {\omega }_0}/2$ and that the response sharpens with increasing j, corroborating that these information measures capture QPTs with precision within the DFT framework. Full article

This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity. Full article

We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage over the thermal Fisher information is attained. These results are explicitly demonstrated for dephasing interactions and also hold for partial swap interactions. Furthermore, we show that the optimal measurements can be performed locally, thus implying that genuine quantum correlations do not play a role in achieving this advantage. We explicitly confirm this by examining the correlation properties for the deterministic collisional model. Full article

It is well known that many quantum information processing methods in artificial atoms depend largely on their engineering properties and their ability to generate quantum correlations. In this paper, we investigate the non-classical correlation dynamics of two trapped ions by using local quantum Fisher information, local quantum uncertainty, as well as logarithmic negativity. The system engineering is designed such that the two-trapped-ions work as two diploe-coupled qubits in a Lamb-Dicke regime. The center-of-mass vibrational modes are initially in coherent/even coherent states. It is found that the two-trapped-ions correlations can be controlled by the Lamb-Dicke nonlinearity, the nonclassicality effect of the initial center-of-mass vibrational mode, as well as the trapped-ion coupling and the intrinsic decoherence. The sudden changes in the non-classical correlations and their stability are shown against Lamb-Dicke nonlinearity, the nonclassicality, the trapped-ion coupling, and the intrinsic decoherence. Full article

In this article, sources of information in electronic states are reexamined and a need for the resultant measures of the entropy/information content, combining contributions due to probability and phase/current densities, is emphasized. Probability distribution reflects the wavefunction modulus and generates classical contributions to Shannon’s global entropy and Fisher’s gradient information. The phase component of molecular states similarly determines their nonclassical supplements, due to probability “convection”. The local-energy concept is used to examine the phase equalization in the equilibrium, phase-transformed states. Continuity relations for the wavefunction modulus and phase components are reexamined, the convectional character of the local source of the resultant gradient information is stressed, and latent probability currents in the equilibrium (stationary) quantum states are related to the horizontal (“thermodynamic”) phase. The equivalence of the energy and resultant gradient information (kinetic energy) descriptors of chemical processes is stressed. In the grand-ensemble description, the reactivity criteria are defined by the populational derivatives of the system average electronic energy. Their entropic analogs, given by the associated derivatives of the overall gradient information, are shown to provide an equivalent set of reactivity indices for describing the charge transfer phenomena. Full article

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information. Full article

In this paper, we study a Hamiltonian system constituted by two coupled two-level atoms (qubits) interacting with a nonlinear generalized cavity field. The nonclassical two-qubit correlation dynamics are investigated using Bures distance entanglement and local quantum Fisher information under the influences of intrinsic decoherence and qubit–qubit interaction. The effects of the superposition of two identical generalized coherent states and the initial coherent field intensity on the generated two-qubit correlations are investigated. Entanglement of sudden death and sudden birth of the Bures distance entanglement as well as the sudden changes in local Fisher information are observed. We show that the robustness, against decoherence, of the generated two-qubit correlations can be controlled by qubit–qubit coupling and the initial coherent cavity states. Full article

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen. Full article

The dynamics of two charged qubits containing Josephson Junctions inside a cavity are investigated under the intrinsic decoherence effect. New types of quantum correlations via local quantum Fisher information and Bures distance norm are explored. We show that we can control the quantum correlations robustness by the intrinsic decoherence rate, the qubit-qubit coupling as well as by the initial coherent states superposition. The phenomenon of sudden changes and the freezing behavior for the local quantum Fisher information are sensitive to the initial coherent state superposition and the intrinsic decoherence. Full article

We investigated numerically the dynamics of quantum Fisher information (QFI) and entanglement for three- and four-level atomic systems interacting with a coherent field under the effect of Stark shift and Kerr medium. It was observed that the Stark shift and Kerr-like medium play a prominent role during the time evolution of the quantum systems. The non-linear Kerr medium has a stronger effect on the dynamics of QFI as compared to the quantum entanglement (QE). QFI is heavily suppressed by increasing the value of Kerr parameter. This behavior was found comparable in the cases of three- and four-level atomic systems coupled with a non-linear Kerr medium. However, QFI and quantum entanglement (QE) maintain their periodic nature under atomic motion. On the other hand, the local maximum value of QFI and von Neumann entropy (VNE) decrease gradually under the Stark effect. Moreover, no prominent difference in the behavior of QFI and QE was observed for three- and four-level atoms while increasing the value of Stark parameter. However, three- and four-level atomic systems were found equally prone to the non-linear Kerr medium and Stark effect. Furthermore, three- and four-level atomic systems were found fully prone to the Kerr-like medium and Stark effect. Full article

The aim of this research was to enhance the classification accuracy of an electronic nose (E-nose) in different detecting applications. During the learning process of the E-nose to predict the types of different odors, the prediction accuracy was not quite satisfying because the raw features extracted from sensors’ responses were regarded as the input of a classifier without any feature extraction processing. Therefore, in order to obtain more useful information and improve the E-nose’s classification accuracy, in this paper, a Weighted Kernels Fisher Discriminant Analysis (WKFDA) combined with Quantum-behaved Particle Swarm Optimization (QPSO), i.e., QWKFDA, was presented to reprocess the original feature matrix. In addition, we have also compared the proposed method with quite a few previously existing ones including Principal Component Analysis (PCA), Locality Preserving Projections (LPP), Fisher Discriminant Analysis (FDA) and Kernels Fisher Discriminant Analysis (KFDA). Experimental results proved that QWKFDA is an effective feature extraction method for E-nose in predicting the types of wound infection and inflammable gases, which shared much higher classification accuracy than those of the contrast methods. Full article