Quantum Mechanical Uncertainty Research Articles

Entropic uncertainty in quantum-state cryptography : A mathematical framework for quantum-resilient encryption

In the escalating race between cryptographic security and quantum computing capabilities, the need for robust encryption methodologies that can withstand the prowess of quantum algorithms is more pressing than ever. This paper introduces a novel cryptographic framework, grounded in the principles of quantum mechanics and the entropic uncertainty principle, to forge a path towards quantum-resilient encryption. At the heart of this approach lies the integration of the entropic uncertainty inherent in quantum states, a fundamental aspect often overlooked in traditional cryptographic strategies. By harnessing this intrinsic uncertainty of quantum mechanics, we propose a mathematical framework that not only challenges the conventional paradigms of encryption but also sets a new benchmark for security in the quantum computing era. The paper delves into the theoretical underpinnings of quantum mechanics relevant to cryptography, with a particular focus on the entropic uncertainty principle. This principle, which posits a natural limit on the precision with which certain pairs of physical properties can be known, serves as the cornerstone of our proposed encryption method. We meticulously develop and outline a mathematical model that leverages this principle, ensuring that the encrypted information remains secure against the formidable computational capabilities of quantum algorithms. We contrast our approach with existing cryptographic methods, highlighting the enhanced security features offered by the entropic uncertainty-based model. The findings underscore the potential of this framework to serve as a resilient encryption mechanism in a landscape increasingly dominated by quantum computing technologies. This research paves the way for a new era of encryption, one that embraces the uncertainty of quantum mechanics as its shield against the threats posed by quantum computing.

Context affects student thinking about sources of uncertainty in classical and quantum mechanics

Context affects student thinking about sources of uncertainty in classical and quantum mechanics

The Primacy of Doubt: From Quantum Physics to Climate Change, How the Science of Uncertainty Can Help Us Understand Our Chaotic World

The Primacy of Doubt: From Quantum Physics to Climate Change, How the Science of Uncertainty Can Help Us Understand Our Chaotic World

Decoherence effects in reactor and Gallium neutrino oscillation experiments: a QFT approach

We adopt the quantum field theoretical method to calculate the amplitude and event rate for a neutrino oscillation experiment, considering neutrino production, propagation and detection as a single process. This method allows to take into account decoherence effects in the transition amplitude induced by the quantum mechanical uncertainties of all particles involved in the process. We extend the method to include coherence loss due to interactions with the environment, similar to collisional line broadening. In addition to generic decoherence induced at the amplitude level, the formalism allows to include, in a straightforward way, additional damping effects related to phase-space integrals over momenta of unobserved particles as well as other classical averaging effects. We apply this method to neutrino oscillation searches at reactor and Gallium experiments and confirm that quantum decoherence is many orders of magnitudes smaller than classical averaging effects and therefore unobservable. The method used here can be applied with minimal modifications also to other types of oscillation experiments, e.g., accelerator based beam experiments.

Uncertainty from the Aharonov–Vaidman identity

In this article, I show how the Aharonov–Vaidman identity Aleft| psi rightrangle = leftlangle A rightrangle left| psi rightrangle + Delta A left| psi ^{perp }_A rightrangle can be used to prove relations between the standard deviations of observables in quantum mechanics. In particular, I review how it leads to a more direct and less abstract proof of the Robertson uncertainty relation Delta A Delta B ge frac{1}{2} left| leftlangle [A,B] rightrangle right| than the textbook proof. I discuss the relationship between these two proofs and show how the Cauchy–Schwarz inequality can be derived from the Aharonov–Vaidman identity. I give Aharonov–Vaidman based proofs of the Maccone–Pati uncertainty relations and show how the Aharonov–Vaidman identity can be used to handle propagation of uncertainty in quantum mechanics. Finally, I show how the Aharonov–Vaidman identity can be extended to mixed states and discuss how to generalize the results to the mixed case.

Possible enhancements of collective flow anisotropy induced by uncertainty relation for fluid element

In the stochastic formulation of viscous hydrodynamics, the velocity of a fluid element fluctuates satisfying a similar relation to the quantum-mechanical uncertainty relation. Using a non-relativistic toy model, we show that the presence of a velocity fluctuation increases the local anisotropy of the momentum distributions of produced hadrons and, consequently, the collective flow parameters such as v 2 are enhanced.

Inverted oscillator: pseudo hermiticity and coherent states

It is known that the standard and the inverted harmonic oscillator are different. Replacing thus ω by ±iω in the regular oscillator is necessary going to give the inverted oscillator H^{r}. This replacement would lead to anti- PT-symmetric harmonic oscillator Hamiltonian (∓iH^{os}). The pseudo-hermiticity relation has been used here to relate the anti-PT-symmetric harmonic Hamiltonian to the inverted oscillator. By using a simple algebra, we introduce the ladder operators describing the inverted harmonic oscillator to reproduce the analytical solutions.We construct the inverted coherent states which minimize the quantum mechanical uncertainty between the position and the momentum. This paper is dedicated to the memory of Omar Djemli and Nouredinne Mebarki who died due to covid 19.

Hawking temperature for 4D-Einstein-Gauss-Bonnet black holes from uncertainty principle

Inspired by string theory, Heisenberg's uncertainty principle can be generalized to include the photon-electron gravitational interaction, which leads to the Generalized Uncertainty Principle (GUP). Although GUP considers gravitational uncertainty at the minimum fundamental length scale in physics, it does not consider the effects of spacetime curvature on quantum mechanical uncertainty relations. The Extended Uncertainty Principle (EUP) is a generalization of Heisenberg's Uncertainty Principle that, unlike the GUP, applies to large length scales. GEUP is also a linear combination of EUP and GUP that creates minimal uncertainty on large length scales. The Einstein-Gauss-Bonnet theory (EGB) can be considered as one of the most promising candidates for modified gravity. In this paper, by using GUP, EUP, and GEUP, we intend to obtain the Hawking temperature of a four-dimensional EGB black hole in the asymptotically flat and (Anti)-de Sitter spacetime. We show that coupling constant, cosmological constant, mass, and radius significantly affect Hawking temperature and decrease or increase Hawking temperature depending on the chosen horizons.

Human Visual System involves macroscopic scaleinvariants and microscopic quantum mechanics single-photon sensitivity

“A half Century has gone by; the general public seems to be lacking a simple Readers’ Digest knowledge about human visual system (HVS). In order to ward off wolf eyesight emitting few photons in a dark cavern, we have evolved to separate the energy from the information, as well as adopt the negation of the converse detection logic. To achieve the sensitivity, HVS uses the dark (no light yet) current, discovered by NIH Hagins, to inhibit 100 rods' bundled together by Ganglion integrator by using its own energy firing. We have applied the dark current to inhibit firing, until a detection of a single photon of wolf eyesight by any of the rod bundle. In this short communication, we shall give 2 theorems: macroscopic scale invariants and microscopic quantum mechanics. Now we know why we can see red color while the other animal cannot and why we can detect a single photon while the other cannot. Given the basic deep learning algorithm and possible experiments to verify Quantum Mechanics Uncertainty Principle for HVS single photon detection capability according to the Gold Standard: Double Blind, Negative Control and Sufficient Statistics.”

Microscopic and macroscopic effects in the decoherence of neutrino oscillations

We present a generic structure (the layer structure) for decoherence effects in neutrino oscillations, which includes decoherence from quantum mechanical and classical uncertainties. The calculation is done by combining the concept of open quantum system and quantum field theory, forming a structure composed of phase spaces from microscopic to macroscopic level. Having information loss at different levels, quantum mechanical uncertainties parameterize decoherence by an intrinsic mass eigenstate separation effect, while decoherence for classical uncertainties is typically dominated by a statistical averaging effect. With the help of the layer structure, we classify the former as state decoherence (SD) and the latter as phase decoherence (PD), then further conclude that both SD and PD result from phase wash-out effects of different phase structures on different layers. Such effects admit for simple numerical calculations of decoherence for a given width and shape of uncertainties. While our structure is generic, so are the uncertainties, nonetheless, a few notable ones are: the wavepacket size of the external particles, the effective interaction volume at production and detection, the energy reconstruction model and the neutrino production profile. Furthermore, we estimate the experimental sensitivities for SD and PD parameterized by the uncertainty parameters, for reactor neutrinos and decay-at-rest neutrinos, using a traditional rate measuring method and a novel phase measuring method.

Ultraviolet-infrared bounds and minimum coupling in effective field theories

We provide a simple new argument for a lower bound on the coupling of a $U(1)$ gauge interaction in an effective field theory (EFT), originally obtained from the weak gravity conjecture. Our argument employs basic principles of quantum mechanical energy-time uncertainty and Lorentz invariance, plus Bekenstein's entropy bound on the ultraviolet (UV) and infrared (IR) scales of an EFT. We show that using an alternative UV-IR relation based on the Cohen-Kaplan-Nelson (CKN) bound results in a stronger lower bound on the $U(1)$ coupling, consistent with the more stringent nature of the CKN relation. Applicability of our reasoning to other interactions is briefly discussed. We also slightly extend the CKN bound, by accounting for the effective degrees of freedom, and examine some of its phenomenological implications.

Measurement of the Magnetic Monopole Charge, the Missing Link in Quantum Mechanics, Aether and the Dark Energy

Charge conservation in the theory of elementary particle physics is one of the best-established principles ‎in physics. As such, if ‎there are magnetic monopoles in the universe, the magnetic charge will most likely be a ‎conserved quantity like electric ‎charges. If neutrinos are magnetic monopoles, as physicists have reported ‎the possibility, the Earth should show signs of ‎having a magnetic monopole charge on a macroscopic scale ‎since neutrons must also have a magnetic monopole charge if ‎the general charge conservation principle is valid. ‎To test this hypothesis, experiments were performed to detect the collective ‎effect of the magnetic monopole ‎charge of neutrons on the earth's equator using two balanced high-strength neodymium rod ‎magnets. We ‎were able to identify the non-zero magnetic monopole charge of the individual neutrons from the experiments. ‎‎The presence of individual magnetic monopole charges in the universe prompted the proposition of the new ‎symmetric form ‎of Maxwell's equations. Based on the theoretical investigation of the new Maxwell's ‎equations, we conclude that magnetic ‎monopole neutrinos are the cause of the origin of quantum ‎mechanical uncertainty, dark energy, and the medium for ‎electromagnetic wave propagation in space.‎‎

The degree of polarization of Raman scattering of light in silicon nanocrystals

Raman scattering of light (RS) on an array of oriented silicon nanocrystals was studied experimentally. The angular dependence of the intensity of the polarized components of the RS was measured and the parameter of the degree of polarization of scattered light was determined. It was found that the degree of polarization of the RS is related to the size of the nanocrystals in the samples. An array of nanocrystals with the same crystallographic orientation was obtained by thermal annealing of a silicon single crystal damaged by ion implantation. During thermal annealing of the sample, the crystallinity of the layer is restored not simultaneously in the entire damaged volume, but in the form of nanocrystals separated by amorphous area. All the clusters formed have the same crystallographic orientation of the original single crystal. The features of the degree of polarization of the RS in nanocrystals are associated with the quantum-mechanical uncertainty of the phonon wave vector and the uncertainty of the phonon direction in a limited volume of the nanocrystal. The relations linking the degree of polarization of the RS with the size of nanocrystals are obtained. A technique for determining the size of nanocrystals by measuring the degree of polarization of the RS is discussed. Keywords: Raman scattering of light, silicon, nanocrystals, ion implantation, annealing, amorphous phase.

Uncertainty Relations in the Madelung Picture.

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

Experimental investigation of the relation between measurement uncertainties and non-local quantum correlations

Bell’s inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell’s inequalities are only possible because the precision of any joint measurement of these observables will be limited by quantum mechanical uncertainty relations. In this paper we explore the relation between the local measurement uncertainties and the magnitude of the correlations by preparing polarization entangled photon pairs and performing joint measurements of non-commuting polarization components at different uncertainty trade-offs. The change in measurement visibility reveals the existence of a non-trivial balance between the measurement uncertainties where the probabilities of a specific pair of measurement outcomes approaches zero because of the particular combination of enhancement and suppression of the experimentally observed correlations. The occurrence of these high-contrast results shows that the quantum correlations between the photons are close to their maximal value, confirming that the Cirel’son bound of Bell’s inequality violations is defined by the minimal uncertainties that limit the precision of joint measurements.

27. USING A TRIO-BASED GENETIC DESIGN FOR INVESTIGATING THE AETIOLOGY OF ATTENTION DEFICIT HYPERACTIVITY DISORDER (ADHD)

Three fundamental pillars for the understanding of virus variation and population dynamics are Darwinian principles, quantum mechanical uncertainties at the atomic level, and internal interactions and network connections among components of an ensemble. In this closing chapter, such general pillars are applied to non-viral systems, in particular prokaryotic and eukaryotic cellular collectivities, and non-genetic systems such as prions. Similarities and differences in the behavior of viruses and cells are analyzed with regard to adaptive molecular mechanisms and consequences for disease treatment. In particular, differences between antiviral resistance and antibiotic resistance, and the possibility of a lethal mutagenesis approach for cancer are examined in the light of concepts exposed in previous chapters for viruses. Clonality in cellular and viral evolution is discussed, with the focus in a distinction between inconsequential and biologically meaningful recombination in the infectious cycles of viruses. The chapter ends with some general considerations on network connections in biological and non-biological systems, with the possibility that the understanding of interactions within viral populations may open new windows for antiviral interventions.

From Rényi Entropy Power to Information Scan of Quantum States.

In this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Rényi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called “cat states”, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.

Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics.

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a “ring polymer” whose spread is related to the quantum mechanical uncertainty in the particle’s position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

The Moral Worlds of Contemporary Realism by Mary K. Holland

The Moral Worlds of Contemporary Realism by Mary K. Holland

Frequency Fluctuations in Tunable and Nonlinear Microwave Cavities

We present a model for how frequency fluctuations comparable to the total cavity linewidth may arise in tunable and nonlinear microwave cavities, and how these fluctuations affect the measurement of scattering matrix elements. Applying this model to the specific case of a two-sided cavity, we obtain closed-form expressions for the average scattering matrix elements in several important cases. A key signature of our model is the subtle deformation of the trajectories swept out by scattering matrix elements in the complex plane. Despite this signature, the fluctuating and non-fluctuating models are qualitatively similar enough to be mistaken for one another. In the case of tunable cavities we show that if one fails to account for these fluctuations then one will find damping rates that appear to depend on the tuning parameter, which is a common observation in such systems. In the case of a Kerr cavity, we show that there exists a fundamental lower bound to the scale of these frequency fluctuations in the steady state, imposed by quantum mechanical uncertainty, which can appreciably affect the apparent damping rates of the cavity as the strength of the nonlinearity approaches the single-photon level. By using the model we present as a fitting function for experimental data, however, one can extract both the true damping rates of the cavity and the effective scale of these frequency fluctuations over the scattering measurement's bandwidth. Lastly, we compare this new method for observing frequency fluctuations to other methods, one of which we extend beyond the regime of small fluctuations.