Uncertainty Principle Research Articles

Uncertainty relations for quantum coherence with respect to mutually unbiased equiangular tight frames

The role of quantum coherence as an information resource has attracted increasing attention in recent years. Many protocols of quantum information science deal with specially selected states. Complete sets of mutually unbiased bases and symmetric informationally complete measurements are widely used in this regard. Other constructions were found to be useful, including projective designs and equiangular tight frames. As a rule, there are additional restrictions on the probabilities generated by quantum measurements assigned to such sets. Inequalities in terms of coherence quantifiers allow one to examine complementarity with respect to different sets. This study aims to examine uncertainty relations for coherence quantifiers averaged with respect to a set of mutually unbiased equiangular tight frames. To quantify the amount of coherence, quantum coherence quantifiers of the Tsallis type and the geometric coherence are used. The first case is induced by the Tsallis relative entropies. The derived inequalities are exemplified with equiangular tight frames of a ququart.

Dimensionless fluctuations balance applied to statistics and quantum physics

This work presents a new method called Dimensionless Fluctuation Balance (DFB), which makes it possible to obtain distributions as solutions of Partial Differential Equations (PDEs). In the first case study, DFB was applied to obtain the Boltzmann PDE, whose solution is a distribution for Boltzmann gas. Following, the Planck photon gas in the Radiation Law, Fermi–Dirac, and Bose–Einstein distributions were also verified as solutions to the Boltzmann PDE. The first case study demonstrates the importance of the Boltzmann PDE and the DFB method, both introduced in this paper. In the second case study, DFB is applied to thermal and entropy energies, naturally resulting in a PDE of Boltzmann’s entropy law. Finally, in the third case study, quantum effects were considered. So, when applying DFB with Heisenberg uncertainty relations, a Schrödinger case PDE for free particles and its solution were obtained. This allows for the determination of operators linked to Hamiltonian formalism, which is one way to obtain the Schrödinger equation. These results suggest a wide range of applications for this methodology, including Statistical Physics, Schrödinger’s Quantum Mechanics, Thin Films, New Materials Modeling, and Theoretical Physics.

Study of first-order quantum corrections of thermodynamics to a Dyonic black hole solution surrounded by a perfect fluid

In this work, we review the metric for a dyonic global monopole with a perfect fluid. To calculate the standard temperature of a Dyonic black hole surrounded by a perfect fluid, we analyze the graphical interpretation of the Hawking temperature concerning the horizon under the effects of the black hole's surrounding field and electric-magnetic charges. For this purpose, we follow the semi-classical method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Lagrangian equation in the presence of quantum gravity as seen in the generalized uncertainty principle (GUP). We calculate the improved temperature of a Dyonic black hole using a bosonic tunneling strategy based on the Hamilton-Jacobi technique. We observe that the physical state of the Dyonic black hole is surrounded by a perfect fluid under the effects of the black hole solution and the gravity parameter. Further, we examine the improved entropy to study the influences of quantum gravity and black hole geometry on entropy. We explore the graphical behavior of entropy based on the black hole's horizon structure and analyze the influence of perfect fluid parameters, electric charge, magnetic charge, and quantum gravity on entropy. Finally, we investigate the unstable and stable conditions of a black hole via graphical results.

Unbounded operators and the uncertainty principle

We study a variant of the uncertainty principle in terms of the annihilation and creation operator on generalized Segal Bargmann spaces, which are used for the FBI-Bargmann transform. In addition, we compute the Berezin transform of these operators and indicate how to use spaces of entire functions in one variable to study the Szegő kernel for hypersurfaces in C 2 \mathbb C^2 .

Lyapunov exponent as a signature of dissipative many-body quantum chaos

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative quantum chaos. For this purpose, we compute analytically the Lyapunov exponent for the vectorized formulation of the large-q limit of a q-body Sachdev-Ye-Kitaev model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of q≥4 based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment. Published by the American Physical Society 2024

Prigogine’s Second Law and Determination of the EUP and GUP Parameters in Small Black Hole Thermodynamics

In 1974, Stephen Hawking made the groundbreaking discovery that black holes emit thermal radiation, characterized by a specific temperature now known as the Hawking temperature. While his original derivation is intricate, retrieving the exact expressions for black hole temperature and entropy in a simpler, more intuitive way without losing the core physical principles behind Hawking’s assumptions is possible. This is obtained by employing the Heisenberg Uncertainty Principle, which is known to be connected to thenvacuum fluctuation. This exercise allows us to easily perform more complex calculations involving the effects of quantum gravity. This work aims to answer the following question: Is it possible to reconcile Prigogine’s second law of thermodynamics for open systems and the second law of black hole dynamics with Hawking radiation? Due to quantum gravity effects, the Heisenberg Uncertainty Principle has been extended to the Generalized Uncertainty Principle (GUP) and successively to the Extended Uncertainty Principle (EUP). The expression for the EUP parameter is obtained by conjecturing that Prigogine’s second law of thermodynamics and the second law of black holes are not violated by the Hawking thermal radiation mechanism. The modified expression for the entropy of a Schwarzschild black hole is also derived.

When will Two Agents Agree on a Quantum Measurement Outcome? Intersubjective Agreement in QBism

In the QBist approach to quantum mechanics, a measurement is an action an agent takes on the world external to herself. A measurement device is an extension of the agent and both measurement outcomes and their probabilities are personal to the agent. According to QBism, nothing in the quantum formalism implies that the quantum state assignments of two agents or their respective measurement outcomes need to be mutually consistent. Recently, Khrennikov has claimed that QBism’s personalist theory of quantum measurement is invalidated by Ozawa’s so-called intersubjectivity theorem. Here, following Stacey, we refute Khrennikov’s claim by showing that it is not Ozawa’s mathematical theorem but an additional assumption made by Khrennikov that QBism is incompatible with. We then address the question of intersubjective agreement in QBism more generally. Even though there is never a necessity for two agents to agree on their respective measurement outcomes, a QBist agent can strive to create conditions under which she would expect another agent’s reported measurement outcome to agree with hers. It turns out that the assumptions of Ozawa’s theorem provide an example for just such a condition.

A universal formulation of uncertainty relation for errors

We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement of statistical nature. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable. Our relation violates the traditional naïve bound ħ/2 for the position-momentum measurement while respecting Heisenberg's original philosophy of the uncertainty principle. Our relation entails, among others, the Arthurs–Kelly–Goodman and Ozawa relations as corollaries to its special cases, and also seamlessly reduces itself to the standard Kennard–Robertson (Schrödinger) relation when the measurement is non-informative.

Emission cells with quantum dots on silicon chip prepared by using fs pulsed laser

Emission efficiency of bulk-silicon is very low due to its indirect-gap of energy band. However, it is interesting that the enhanced emission has been observed in the micro-cavities array fabricated by using femtosecond (fs) pulsed laser, in which the stimulated emission characteristics occur after annealing for suitable time in the photo-luminescence (PL) measurement at room temperature. The results of experiment and calculation demonstrated that the enhanced emission may be originated from the Si quantum dots embedded in the micro-cavities prepared by fs pulsed laser. Here, the direct-gap of energy band appears after annealing due to the Heisenberg principle related to ⊿k–1/⊿x in quantum system of nanostructures. The PL intensity obviously increases on the Si quantum dots growing with annealing for better crystallization, in which the external quantum efficiency is higher than 40 % near 760 nm. A new kind of emission source of the micro-cavities array in visible wavelength has been built on silicon wafer, in which the Si quantum dots play a main role for enhancement of emission. It should have a good application in optical integrated chip based on silicon, such as emission cells built on Si chip.

Structural study of the intrinsically disordered tardigrade damage suppressor protein (Dsup) and its complex with DNA

Studies of proteins, found in one of the most stress-resistant animals tardigrade Ramazzottius varieornatus, aim to reveal molecular principles of extreme tolerance to various types of stress and developing applications based on them for medicine, biotechnology, pharmacy, and space research. Tardigrade DNA/RNA-binding damage suppressor protein (Dsup) reduces DNA damage caused by reactive oxygen spices (ROS) produced upon irradiation and oxidative stresses in Dsup-expressing transgenic organisms. This work is focused on the determination of structural features of Dsup protein and Dsup-DNA complex, which refines details of protective mechanism. For the first time, intrinsically disordered nature of Dsup protein with highly flexible structure was experimentally proven and characterized by the combination of small angle X-ray scattering (SAXS) technique, circular dichroism spectroscopy, and computational methods. Low resolution models of Dsup protein and an ensemble of conformations were presented. In addition, we have shown that Dsup forms fuzzy complex with DNA.

Traces of Quantum Gravity Effects at Late-time Cosmological Dynamics via Distance Measures

Inspired by the entropy–area relation of black hole thermodynamics, we study the thermodynamics of the cosmological apparent horizon in a spatially flat Friedmann–Robertson–Walker universe in the framework of an extended uncertainty principle (EUP). The adopted EUP naturally admits a minimal measurable momentum (equivalently a maximal measurable length), as an infrared cutoff in the theory. We derive the modified Friedmann equations in this setup and explore some predictions of these equations for the late-time universe via distance measures. We show that in this framework it is possible to realize the late-time cosmic speedup and transition to the phantom phase of the equation-of-state parameter of the effective cosmic fluid without recourse to any dark energy component or modified gravity. Inspection of various distance measures in this framework shows that an EUP with a negative deformation parameter suffices for the interpretation of the late-time asymptotically de Sitter universe with standard nonrelativistic matter.

Network analysis for the steady-state thermodynamic uncertainty relation

Network analysis for the steady-state thermodynamic uncertainty relation

Entropic Uncertainty Relations and Mutual Information Correlation Sums in Two-level Superposition States of Coupled Oscillators

The effects of quantum interferences and interaction strength on the entropic uncertainty relations, and on mutual information correlation sums, are examined in two-level superposition states of two coupled oscillators. The presence of quantum interferences results in a movement of the entropy sums toward the uncertainty relation bound, for both attractive and repulsive interaction potentials. On the other hand, these interferences suppress the statistical correlations in the presence of an attractive potential, while the correlations increase for a repulsive one. In general, stronger interactions between particles move the entropy sums away from bound, with the result that the systems possess larger statistical correlations. However, there are superposition and attractive interaction regimes, where the entropy sum of an interacting system can actually lie closer to the bound, in comparison to the corresponding non-interacting one. In these cases, the statistical correlations between particles is lesser for the interacting systems, as compared to the non-interacting ones. These effects are not observed when repulsive potentials are present. Here, the non-interacting systems lower-bound both the entropy sums and correlation measures. These results offer insights into the nature of superposition or quantum interference effects in interacting quantum systems, and the behavior in terms of the entropic uncertainty relations, statistical correlations and interaction strength. Resumen. Se examinan los efectos que las interferencias cuánticas y la magnitud de la interacción tienen sobre las relaciones de incertidumbre entrópicas, así como sobre las sumas correlaciones me didas a través de la información mutua, en estados de superposición de dos niveles de dos osciladores acoplados. La presencia de interferencias cuánticas da como resultado un movimiento de las sumas entrópicas hacia la cota de la relación de incertidumbre, tanto para potenciales de interacción atractivos como repulsivos. Por otra parte, en presencia de un potencial atractivo, estas interferencias suprimen las correlaciones estadísticas, mientras que las correlaciones aumentan en presencia de uno repulsivo. En general, con interacciones más fuertes entre partículas, las sumas de entrópicas se alejan de la cota, dando como resultado mayores correlaciones estadísticas en los sistemas. Sin embargo, existen regímenes de superposición e interacción atractiva, en los cuales la suma entrópica de un sistema interactuante puede estar más cerca de la cota, en comparación con el sistema no interactuante correspondiente. En estos casos, las correlaciones estadísticas entre partículas son menores para los sistemas interactúantes que para los no interactuantes. Estos efectos no se observan en los potenciales repulsivos. En este caso, los sistemas no interactuantes establecen límites inferiores tanto para las sumas entrópicas como para las medidas de correlación. Estos resultados dan información sobre la naturaleza de los efectos de superposición o interferencia cuántica en sistemas cuánticos interactuantes, y su comportamiento en términos de relaciones de incertidumbre entrópica, correlaciones estadísticas y fuerza de interacción.

Pascal's uncertainty principle: Managing drug–drug interactions when the risks are unclear

AbstractTherapeutic decision‐making (TDM) often occurs under conditions of scientific uncertainty, including decisions on how to manage the majority of drug–drug interactions (DDIs). The existence of many DDIs is not firmly established, and there is an unfortunate tendency to make decisions based on the binary assessment of whether or not a particular DDI is real, rather than taking a more probabilistic and holistic approach to TDM. There also seems to be an undue fear of making a Type I error (assuming the DDI is real when it is not) while ignoring the often much greater risk of a Type II error (assuming the DDI is not real, when it is). Thus, a more rational TDM process for such DDIs is needed. In his famous “Wager,” philosopher‐mathematician Blaise Pascal made a probabilistic argument for believing in God. Instead of considering probability in isolation, Pascal linked the probability of God's existence with the severity of the outcome (an eternity in Hell for non‐believers) and also added a third factor—the ease with which the risk can be avoided. We propose a novel paradigm for TDM that uses all three of Pascal's steps: probability, severity, and avoidability. We present several specific DDI examples to demonstrate how Pascal's Uncertainty Principle can help pharmacists make clinical management decisions for these DDIs. We suggest that this process be called “Pascal's Uncertainty Principle” rather than “Pascal's Wager,” because it can be used to make rational decisions in the presence of uncertainty in many non‐theological situations. This process reinforces the value of philosophical training for pharmacy students.

Schrdinger equation for various quantum systems based on Heisenberg's uncertainty principle

This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.

Schrdinger equation for various quantum systems based on Heisenberg's uncertainty principle

This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.

Harmonic analysis approach to the proof of Heisenberg inequality

the Heisenberg uncertainty Principle is a fundamental principle in quantum mechanics, which was developed by the German physicist Werner Heisenberg and was proposed by him in 1927. This principle states that for a pair of physical quantities that share phase space, such as position and momentum, it is impossible to accurately measure their values at the same time. There are several variants of it in harmonic analysis studies, and the article will introduce some of them in R^1 space and L^2 space. In the process of providing the Heisenberg inequality, the article proved the Plancherel identity and Schwartz inequality by using Fourier transform and inverse Fourier transform. Finally, author solved the equation of the wave function (x) . The famous physicists Heisenberg proposed one of the more novel ideas in quantum mechanics the existence of unobservable orbits cannot be assumed, which did bring great influence in quantum mechanics. The article will introduce the conception of Heisenberg inequality and try to finish the proof.

Harmonic analysis approach to the proof of Heisenberg inequality

the Heisenberg uncertainty Principle is a fundamental principle in quantum mechanics, which was developed by the German physicist Werner Heisenberg and was proposed by him in 1927. This principle states that for a pair of physical quantities that share phase space, such as position and momentum, it is impossible to accurately measure their values at the same time. There are several variants of it in harmonic analysis studies, and the article will introduce some of them in R^1 space and L^2 space. In the process of providing the Heisenberg inequality, the article proved the Plancherel identity and Schwartz inequality by using Fourier transform and inverse Fourier transform. Finally, author solved the equation of the wave function (x) . The famous physicists Heisenberg proposed one of the more novel ideas in quantum mechanics the existence of unobservable orbits cannot be assumed, which did bring great influence in quantum mechanics. The article will introduce the conception of Heisenberg inequality and try to finish the proof.

Casimir wormholes with GUP correction in the Loop Quantum Cosmology

In this paper, we obtain novel traversable, static, and spherically symmetric wormhole solutions, derived from the effective energy density and isotropic pressure resulting from the Casimir effect, corrected by the Generalized Uncertainty Principle (GUP) within the framework of Loop Quantum Cosmology (LQC). The goal is to explore the interplay between competing quantum gravity effects and quantum vacuum phenomena in the emergence of non-trivial spacetime structures. We examine features such as traversability, embedding diagrams, energy conditions, curvature, and stability of the obtained solutions. Additionally, we analyze the junction conditions required to integrate the wormhole spacetime with an external Schwarzschild spacetime and calculate the amount of exotic matter needed to maintain the wormhole. Finally, we evaluate the conditions under which this latter remains visible or is hidden by the event horizon associated with the Schwarzschild spacetime.

Tradeoff relations in open quantum dynamics via Robertson, Maccone–Pati, and Robertson–Schrödinger uncertainty relations

Abstract The Heisenberg uncertainty relation, together with Robertson’s generalisation, serves as a fundamental concept in quantum mechanics, showing that noncommutative pairs of observables cannot be measured precisely. In this study, we explore the Robertson-type uncertainty relations to demonstrate their effectiveness in establishing a series of thermodynamic uncertainty relations and quantum speed limits in open quantum dynamics. The derivation utilises a scaled continuous matrix product state representation that maps the time evolution of the quantum continuous measurement to the time evolution of the system and field. Specifically, we consider the Maccone–Pati uncertainty relation, a refinement of the Robertson uncertainty relation, to derive thermodynamic uncertainty relations and quantum speed limits. These newly derived relations, which use a state orthogonal to the initial state, yield bounds that are tighter than previously known bounds. Moreover, we consider the Robertson–Schrödinger uncertainty, which extends the Robertson uncertainty relation. Our findings not only reinforce the significance of the Robertson-type uncertainty relations, but also expand its applicability in identifying uncertainty relations in open quantum dynamics.