Search Results (72)

The quantizer–dequantizer method is employed. Using the construction of probability distributions describing density operators of a quantum system states, the connection between the Feynman path integral and the time evolution of the density operator (Landau density matrix) as well as the wave function of the stateconsidered. For single–mode systems with continuous variables, a tomographic propagator is introduced in the probability representation of quantum mechanics. An explicit expression for the probability in terms of the Green function of the Schrödinger equation is obtained. Equations for the Green functions defined by arbitrary integrals of motion are derived. Examples of probability distributions describing the evolution of state of a free particle, as well as states of systems with integrals of motion that depend on time (oscillator type) are discussed. Full article

This work presents and evaluates two threshold-based detection methods for the Six-State quantum key distribution protocol, considering a realistic scenario involving partial intercept–resend attack and channel noise. The statistical properties of the shared quantum bit error rate (QBER) are analyzed and used to estimate the attacker interception density from observed data. Building on this foundation, the work derives two optimal QBER detection thresholds designed to minimize both false positive and false negative rates, following, respectively, upper theoretical bounds and limit probability density function approach. A developed Qiskit simulation environment enables the evaluation and comparison of the two detection methods on simulated and real-inspired quantum systems with differing noise characteristics. This framework moves beyond theoretical analysis, allowing practical investigation of system noise effects on detection accuracy. Simulation results confirm that both methods are robust and effective, achieving high detection accuracy across all the tested configurations, thereby validating their applicability to real-world quantum communication systems. Full article

The present work discusses the birth of the Universe via quantum tunneling through a potential barrier, based on quantum cosmology, taking a running cosmological constant into account. We consider the Friedmann–Lemaître–Robertson–Walker (FLRW) metric with positively curved spatial sections ($k=1$) and the matter’s content is a dust perfect fluid. The model was quantized by the Dirac formalism, leading to a Wheeler–DeWitt equation. We solve that equation both numerically and using a WKB approximation. We study the behavior of tunneling probabilities $T{P}_{WKB}$ and $T{P}_{int}$ by varying the energy E of the dust perfect fluid, the phenomenological parameter $\nu$, the present value of the Hubble function $H_0$, and the constant energy density ${\rho }_{\Lambda }^0$, with the last three parameters all being associated with the running cosmological constant. We observe that both tunneling probabilities, $T{P}_{WKB}$ and $T{P}_{int}$, decrease as one increases $\nu$. We also note that $T{P}_{WKB}$ and $T{P}_{int}$ grow as E increases, indicating that the Universe is more likely to be born with higher dust energy E values. The same is observed for the parameter ${\rho }_{\Lambda }^0$, that is, $T{P}_{WKB}$ and $T{P}_{int}$ are larger for higher values of ${\rho }_{\Lambda }^0$. Finally, the tunneling probabilities decrease as one increases the value of $H_0$. Therefore, the best conditions for the Universe to be born, in the present model, would be to have the highest possible values for E and $\Lambda$ and the lowest possible values for $\nu$ and $H_0$. Full article

Wigner functions are a distribution function on phase space that allow to represent the state of a quantum-mechanical system. They are in many ways similar to classical phase space probability distributions, but can, in contrast to these, be negative. A description of a quantum system in terms of Wigner functions is equivalent to the more widely used one in terms of density operators or wave functions, but has advantages in visualizing properties of a quantum state and in studying the quantum–classical transition. Full article

In this study, we employed density functional theory (DFT), a standard method in quantum chemistry, to investigate the structural intricacies of thioether-linked naphthalene-based liquid-crystal dimers. The theoretical analysis included the calculation of the molecular bend angle, a crucial factor influencing the formation of the twist–bend nematic (N_TB) phase, as well as other molecular parameters such as transition dipole moments, bond lengths, and bond energies. These calculations allowed for the determination of the probable conformations and the computation of their vibrational spectra, which are essential for interpreting experimental spectra. Connecting these insights, we identified stable conformations and observed differences in the spectra between the conventional nematic (N) and N_TB phases. The combined DFT calculations and infrared absorbance measurements allowed us to investigate the structure and intermolecular interactions of molecules in the N and N_TB phases of the dimers. Notably, significant changes in average absorbance were detected in the experimental spectra in the N_TB phase. During the transition from the N phase to the N_TB phase, a clear decrease in absorbance for longitudinal dipoles and an increase for transverse dipoles were observed. This phenomenon suggests that longitudinal dipoles are antiparallel, while transverse dipoles are parallel. To verify the influence of nearest-neighbor interactions, DFT calculations were conducted on a system comprising several neighboring molecules. Full article

We show that the theory of quantum statistical mechanics is a special model in the framework of the quantum probability theory developed by mathematicians, by extending the characteristic function in the classical probability theory to the quantum probability theory. As dynamical variables of a quantum system must respect certain commutation relations, we take the group generated by a Lie algebra constructed with these commutation relations as the bridge, so that the classical characteristic function defined in a Euclidean space is transformed to a normalized, non-negative definite function defined in this group. Indeed, on the quantum side, this group-theoretical characteristic function is equivalent to the density matrix; hence, it can be adopted to represent the state of a quantum ensemble. It is also found that this new representation may have significant advantages in applications. As two examples, we show its effectiveness and convenience in solving the quantum-optical master equation for a harmonic oscillator coupled with its thermal environment, and in simulating the quantum cat map, a paradigmatic model for quantum chaos. Other related issues are reviewed and discussed as well. Full article

We present a theoretical analysis of the experimental data reported by Ichikawa et al. on the spatial distribution of ultracold neutrons in the Earth’s gravitational field above a mirror. The data involve a projection onto a pixelated detector via scattering by a cylindrical mirror. Our study includes a calculation of the theoretical spatial distribution of the probability density associated with the quantum gravitational states of ultracold neutrons. Furthermore, we analyze this spatial distribution using the Wigner function framework. Based on our analysis, we cannot confirm that the experimental data reported by Ichikawa et al. correspond to the spatial distribution of quantum gravitational states of ultracold neutrons. Full article

The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given reduced version. Without a specification of relevant details of the environment, the time evolution of a reduced density matrix is therefore typically unpredictable, even if the dynamics of the full density matrix are deterministic. With this in mind, we investigate a two-level open quantum system using a framework of quantum state diffusion. We consider the pseudorandom evolution of its reduced density matrix when subjected to an environment-driven process that performs a continuous quantum measurement of a system observable, invoking dynamics that asymptotically send the system to one of the relevant eigenstates. The unpredictability is characterised by a stochastic entropy production, the average of which corresponds to an increase in the subjective uncertainty of the quantum state adopted by the system and environment, given the underspecified dynamics. This differs from a change in von Neumann entropy, and can continue indefinitely as the system is guided towards an eigenstate. As one would expect, the simultaneous measurement of two non-commuting observables within the same framework does not send the system to an eigenstate. Instead, the probability density function describing the reduced density matrix of the system becomes stationary over a continuum of pure states, a situation characterised by zero further stochastic entropy production. Transitions between such stationary states, brought about by changes in the relative strengths of the two measurement processes, give rise to finite positive mean stochastic entropy production. The framework investigated can offer useful perspectives on both the dynamics and irreversible thermodynamics of measurement in quantum systems. Full article

We explore some consequences of modifying the usual Heisenberg commutation relations of two simple systems: first, the one-dimensional quantum system given by the infinite square-well potential, and second, the case of a gas of N non-interacting particles in a box of volume V, which permit obtaining analytical solutions. We analyse two possible cases of modified Heisenberg commutation relations: one with a linear and non-linear dependence on the position and another with a linear and quadratic dependence on the momentum. We determine the eigenfunctions, probability densities, and energy eigenvalues for the one-dimensional square well for both deformation cases. For linear and non-linear x deformation dependence, the wave functions and energy levels change substantially when the weight factor associated with the modification term increases. Here, the energy levels are rescaled homogeneously. Instead, for linear and quadratic momentum p deformation dependence, the changes in the energy spectrum depend on the energy level. However, the probability densities are the same as those without any modification. For the non-interacting gas, the position deformation implies that the ideal gas state equation is modified, acquiring the form of a virial expansion in the volume, whereas the internal energy is unchanged. Instead, the ideal gas state equation remains unchanged at the lowest order in $\beta$ for the momentum modification case. However, the temperature modifies the internal energy at the lowest order in $\beta$. Thus, this study indicates that gravity could generate forces on particles by modifying the Heisenberg commutation relations. Therefore, gravitation could be the cause of the other three forces of nature. Full article

Aluminum (Al) ion implantation is one of the most important technologies in SiC device manufacturing processes due to its ability to produce the p-type doping effect, which is essential to building p–n junctions and blocking high voltages. However, besides the doping effect, defects are also probably induced by the implantation. Here, the impacts of Al ion implantation-induced defects on 4H-SiC MOSFET channel transport behaviors are studied using a multiscale simulation flow, including the molecular dynamics (MD) simulation, density functional theory (DFT) calculation, and tight-binding (TB) model-based quantum transport simulation. The simulation results show that an Al ion can not only replace a Si lattice site to realize the p-doping effect, but it can also replace the C lattice site to induce mid-gap trap levels or become an interstitial to induce the n-doping effect. Moreover, the implantation tends to bring additional point defects to the 4H-SiC body region near the Al ions, which will lead to more complicated coupling effects between them, such as degrading the p-type doping effect by trapping free hole carriers and inducing new trap states at the 4H-SiC bandgap. The quantum transport simulations indicate that these coupling effects will impede local electron transports, compensating for the doping effect and increasing the leakage current of the 4H-SiC MOSFET. In this study, the complicated coupling effects between the implanted Al ions and the implantation-induced point defects are revealed, which provides new references for experiments to increase the accepter activation rate and restrain the defect effect in SiC devices. Full article

This study focused on developing an innovative, straightforward, and economical method utilizing a mixture of readily available solvents to extract arborescin (C₂OH₂OO₈) crystals from Artemisia absinthium L. (A. absinthium). The structural elucidation and characterization were conducted using a suite of techniques including IR spectroscopy, CNHSO elemental analysis, scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDS), and mass spectroscopy (MS). Density functional theory (DFT) calculations were employed to determine the molecular properties. Antioxidant activity was measured using the DPPH radical scavenging assay and the β-carotene bleaching test. Antimicrobial efficacy was assessed against four bacterial strains and three fungal strains. The molecular docking approach was employed to predict the probable binding patterns and affinities of arborescin with specific target biomolecules. Employing an array of analytical techniques, examination of the isolated crystal from A. absinthium. led to its comprehensive structural elucidation. IR spectroscopy revealed the presence of distinctive functional groups, including a carbonyl group within the γ-lactone and an epoxy group. CNHSO elemental analysis verified that the crystal contained only carbon, hydrogen, and oxygen, a finding corroborated by SEM-EDS analysis, consistent with the molecular structure of arborescin. Additionally, mass spectrometry confirmed the identity of the compound as arborescin, with a molecular ion with a mass m/z = 248. Quantum-Chemical Descriptors revealed that arborescin is resistant to elementary decomposition under standard conditions. Although arborescin demonstrates a relatively low antioxidant capacity, with an IC50 of 5.04 ± 0.12 mg/mL in the DPPH assay, its antioxidant activity in the β-carotene bleaching test was found to be 3.64%. Remarkably, arborescin effectively inhibits the growth of Staphylococcus aureus and Listeria innocua at low concentrations (MIC = 166 µg/mL). Additionally, it exhibits significant antifungal activity against Candida glabrata, with a minimum inhibitory concentration (MIC) and minimum fungicidal concentration (MFC) of 83 µg/mL and 166 µg/mL, respectively. In this study, arborescin exhibited a robust docking score of −8.1 kcal/mol, indicating a higher affinity compared to ciprofloxacin. This suggests that arborescin has significant potential as a potent antibacterial agent. Full article

With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions $\mathcal{N}$ ($\mu$, ${\sigma }_0)$, as before, but with a constant ${\sigma }_0$ not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution ${\mathcal{N}}_m(\mathit{\mu },{\mathbf{\Sigma }}_0)$ with a constant variance–covariance matrix ${\mathbf{\Sigma }}_0$ not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger’s equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of ${\sigma }_0$, altogether leading to the concept of “intrinsic”. Similarly, as in our previous work with the estimator’s variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the “intrinsic” Cramér–Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of “intrinsic” information-theoretic models, which are essential for developing physics. Full article

This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be “quantum”. Full article

We have recently shown that the critical Anderson electron in $D=3$ dimensions effectively occupies a spatial region of the infrared (IR) scaling dimension $d_{\mathrm{IR}}\approx 8/3$. Here, we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probabilities, such that the points comprising a region are of similar relevance, and calculate the IR scaling dimension d of each. This allows us to infer the probability density $p\left(d\right)$ for dimension d to be accessed by the electron. We find that $p\left(d\right)$ has a strong peak at d very close to two. In fact, our data suggest that $p\left(d\right)$ is non-zero on the interval $[d_{\min },d_{\max }]\approx [4/3,8/3]$ and may develop a discrete part ($\delta$-function) at $d=2$ in the infinite-volume limit. The latter invokes the possibility that a combination of quantum mechanics and pure disorder can lead to the emergence of integer (topological) dimensions. Although $d_{\mathrm{IR}}$ is based on effective counting, of which $p\left(d\right)$ has no a priori knowledge, $d_{\mathrm{IR}}\ge d_{\max }$ is an exact feature of the ensuing formalism. A possible connection of our results to the recent findings of $d_{\mathrm{IR}}\approx 2$ in Dirac near-zero modes of thermal quantum chromodynamics is emphasized. Full article

This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space of a smooth statistical manifold of normal probability distributions. Following this approach, we study the stationary states with the time-independent Schrödinger’s equation to discover that the information could be represented and distributed over a set of quantum harmonic oscillators, one for each independent source of data, whose coordinate for each oscillator is a parameter of the smooth statistical manifold to estimate. We observe that the estimator’s variance equals the energy levels of the quantum harmonic oscillator, proving that the estimator’s variance is definitively quantized, being the minimum variance at the minimum energy level of the oscillator. Interestingly, we demonstrate that quantum harmonic oscillators reach the Cramér–Rao lower bound on the estimator’s variance at the lowest energy level. In parallel, we find that the global probability density function of the collective mode of a set of quantum harmonic oscillators at the lowest energy level equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. Interestingly, the opposite is also true, as the prior is constant. Altogether, these results suggest that we can break the sources of information into little elements: quantum harmonic oscillators, with the square modulus of the collective mode at the lowest energy representing the most likely reality, supporting A. Zeilinger’s recent statement that the world is not broken into physical but informational parts. Full article