Uncertainty Principle Research Articles

Analysis Of Wasatiyyah Thoughts Of Muhammad Mahfudh Tarmadzi's On Takfirism In His Is'af Al Mathali'

Wasatiyyah thinking, or moderation, is an essential principle in Islamic teachings which prioritizes balance and tolerance in religious life. This concept becomes very relevant amidst the challenges of extremism and intolerance modern society faces. Muhammad Mahfudh Tarmadzi, a great Indonesian cleric, made a significant contribution through his work Is'af al-Mathali', which offers a moderate view in dealing with the phenomenon of takfirism, an ideology that disbelieves fellow Muslims. This research aims to explore Wasatiyyah Mahfudh Tarmadzi's thoughts, focusing on its application in overcoming the issue of takfirism. This research uses a text analysis methodology on Is'af al-Mathali's work to understand the application of balance, justice, and tolerance principles in responding to contemporary religious issues, especially takfirism. Mahfudh Tarmadzi strongly criticized the practice of takfirism, emphasizing the importance of solid evidence and a fair process in accusing infidels because takfirism often triggers conflict and violence among Muslims. The main aim of this research is to emphasize the relevance of Wasatiyyah Mahfudh Tarmadzi's thoughts in facing current religious challenges, especially in countering takfirism. This research also aims to examine Mahfudh Tarmadzi's contribution to promoting a more harmonious and peaceful religious life. It is hoped that the research results will provide in-depth insight into the importance of Wasatiyyah in building a tolerant society amidst the threat of extremism and radicalism

Spherical Logvinenko–Sereda–Kovrijkine type inequality and null-controllability of the heat equation on the sphere

It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko–Sereda–Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spectral inequality for the Laplace–Beltrami operator, which, in turn, yields observability and null-controllability with explicit estimates on the control costs for the spherical heat equation that are sharp in the large and in the small time regime.

Steered quantum coherence and entropic uncertainty relation in the cluster Ising model

Abstract In this paper, we investigate the cluster Ising model (CIM) via steered quantum coherence (SQC) and entropic uncertainty relation (EUR). We present the behavior of SQC quantified by the L1 norm, relative entropy and quantum Jensen–Shannon divergence. We also demonstrate the properties of EUR in the CIM. In addition, we provide a comparative analysis of these measures and present detailed numerical results.

Emergence of squeezed coherent states in Kaluza–Klein cosmology

In this work, we consider a propagating scalar field on Kaluza–Klein-type cosmological background. It is shown that this geometrical description of the Universe resembles – from a Hamiltonian standpoint – a damped harmonic oscillator with mass and frequency, both time-dependents. In this scenario, we construct the squeezed coherent states (SCSs) for the quantized scalar field by employing the invariant operator method of Lewis–Riesenfeld (non-Hermitian) in a non-unitary approach. The non-classicality of SCSs has been discussed by examining the quadrature squeezing properties from the uncertainty principle. Moreover, we compute the probability density, which allows us to investigate whether SCSs can be used to seek traces of extra dimensions. We then analyze the effects of the existence of supplementary space on cosmological particle production in SCSs by considering different cosmological eras.

Incorporating the cosmological constant in a modified uncertainty principle

This study explores the cosmological constant problem and modified uncertainty principle within a unified framework inspired by a void-dominated scenario for cosmology. In a recent paper [E. Yusofi, M. Khanpour, B. Khanpour, M. A. Ramzanpour and M. Mohsenzadeh, Mon. Not. R. Astron. Soc. 511, L82 (2022)], voids were modeled as spherical bubbles of similar average sizes, and the surface energy on the voids’ borders was calculated across various scales in a heuristic manner. We show that these result in a significant discrepancy of approximately [Formula: see text] between the cosmological constant values from the minimum to the maximum radii of bubbles. Furthermore, when considering the generalized form of the uncertainty principle with both minimum and maximum lengths, i.e. [Formula: see text], a similar order of discrepancy is observed between [Formula: see text] and [Formula: see text], indicating that [Formula: see text]. As a primary outcome of this finding, we offer a novel uncertainty principle that incorporates a nonzero cosmological constant.

Complexity measures of electric screening effect in interstellar medium

Using the screening potential, we explore probability density properties in interstellar mediums (ISM) in information theory. With the eigenfunctions obtained for the screening potential using the Schrodinger equation, we studied the probability distribution for Shannon entropy, Fisher information, and their complexity measures for the values of n and l. From our numerical result, for Shannon entropy, we observed a more localized probability distribution in position and a decreasing localization in the momentum space as the values of n and l increases. For Fisher information, localization increases in the position space and, consequently, delocalization in their momentum spaces. The uncertainty relations of Shannon entropy and Fisher information were computed and satisfied the relations. For interstellar mediums, our findings align with Heinsberg’s uncertainty principle. Complexity measure was also studied for the interstellar mediums and our findings showed increasing disorder in the position space for increasing values of n and l. Furthermore, we extended the Debye-Hückel length to other regimes particularly, Magnetosphere (D=102) and Intergalactic Mediums (D=105)

Relative entropy based uncertainty principles for graph signals

In physical quantum mechanics, the uncertainty principle in presence of quantum memory [Berta M, Christandl M, Colbeck R,et al., Nature Physics] can reach much lower bound, which has resulted in a huge breakthrough in quantum mechanics. Inspired by this idea, this paper would propose some novel uncertainty relations in terms of relative entropy for signal representation and time-frequency resolution analysis. On one hand, the relative entropy measures the distinguishability between the known (priori) basis and the client basis, which implies that we have partial “memory” of the client basis so that the uncertainty bounds become sharper in some cases. On the other hand, in some cases, if the reference basis along with nearly the same energy distribution could be given, then the uncertainty bound would tend to zero, as shows that there is no uncertainty any longer. These novel uncertainty relationships with sharper bounds would give us the potential advantages over the classical counterpart. In addition, the detailed comparison with classical Shannon entropy based uncertainty principle has been addressed as well via combined uncertainty relations. Finally, the theoretical analysis and numerical experiments on certain application over graph signals have been demonstrated to show the efficiency of these proposed relations.

Non-classical correlations and coherence in a two-dimensional electron gas under the influence of Rashba spin–orbit coupling

This investigation delves into the dynamics of quantum correlations and coherence within a two-dimensional electron gas (2DEG) system, taking into account the influence of Rashba spin–orbit coupling (SOC). We utilize metrics such as logarithmic negativity ([Formula: see text]), local quantum uncertainty (LQU ([Formula: see text])), and relative entropy of coherence ([Formula: see text]) to specifically assess these quantum resources among electron spins within non-interacting electron gases. Our study investigates how the separation distance (R) between electrons and the intensity of Rashba SOC ([Formula: see text]), impact the behavior of quantum properties within the 2DEG system. We find that specific strengths of Rashba SOC can effectively regulate quantum correlations and coherence within this system. Particularly significant is our observation that optimal quantum indicators emerge when electron proximity is minimized, underscoring the substantial influence of electron distance on quantum characteristics. Conversely, as electron separation increases, these quantum metrics diminish. Therefore, by adjusting the Rashba parameter, we can enhance the resilience of these quantum measurements against increasing electron separations, providing valuable insights into the potential for controlling and manipulating quantum behavior in similar 2DEG systems.

Entropic uncertainty relations and quantum Fisher information of top quarks in a large hadron collider

Entropic uncertainty relations and quantum Fisher information of top quarks in a large hadron collider

Mutual estimates of time-frequency representations and uncertainty principles

Mutual estimates of time-frequency representations and uncertainty principles

Entropic uncertainty relations and entanglement detection from quantum designs

Abstract Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information theory. In this article, we investigate entropic uncertainty relations and entanglement detection with an emphasis on quantum measurements with design structures. On the one hand, we derive improved Rényi entropic uncertainty relations for design-structured measurements, exploiting the property that the sum of powered (e.g., squared) probabilities of obtaining different measurement outcomes is now invariant under unitary transformations of the measured system and can be easily computed. On the other hand, the above property essentially imposes a state-independent upper bound, which is achieved at all pure states, on one’s ability to predict local outcomes when performing a set of design-structured measurements on quantum systems. Realizing this, we also obtain criteria for detecting multi-partite entanglement with design-structured measurements.

Biquaternion ambiguity function and associated uncertainty principles

A mathematical tool used to analyze signals in high-dimensional areas is the biquaternion ambiguity function. While typical ambiguity functions deal with time delay and Doppler frequency, biquaternion ambiguity functions extend the concept to rotations and scaling factors. Biquaternion ambiguity functions offer a more thorough representation of signal ambiguity in these high-dimensional spaces, which can help develop better signal processing algorithms for a range of uses. In this paper, we introduce the notion of biquaternion ambiguity function which is formed from conventional ambiguity function by invoking biquaternion algebra. We first establish the various properties, namely dilation, translation, shift, nonlinearity, boundedness, reconstruction formula, Moyal’s formula, and inversion formula. An interesting relationship between the biquaternion Fourier transform and the biquaternion ambiguity function is also established. Furthermore, we establish the various versions of uncertainty inequalities namely, Pitt’s inequality, sharp Hausdorff–Young inequality, sharp Local uncertainty principle and logarithmic uncertainty principle for biquaternion ambiguity function. Some potential applications are also presented at the end.

Values of Coexistence in Islamic Civilization: The Relationship with Others and the Challenge of Extremism

This study employs a descriptive-analytical method to emphasize the genuineness and importance of peaceful coexistence values among religions and cultures in Islamic civilization. It specifically focuses on the interaction with others, living together, acknowledging, respecting, and collaborating with them in different aspects of shared humanity. This research examines the language of extremism by studying and analyzing it, seeing it as the primary obstacle to the principles of civic coexistence and tolerance. The research findings indicate that the key factor that sets apart the principles of peaceful coexistence among individuals, irrespective of their religious and racial backgrounds, and that necessitates the acceptance of others in Islamic ideology, is the perception of such acceptance as legitimate obligations. An individual is recognized as a Muslim only when they openly acknowledge their adherence to the Islamic faith. Through the analysis of holy writings and the Prophet's biography, the researcher concludes that any radical and divisive rhetoric that promotes the rejection of peaceful coexistence cannot be regarded as Islamic speech, and does not accurately reflect Islam and Muslims. Instead, it is an extreme rhetoric that only represents its advocates, a rhetoric that Islam disavows, just as it disavows other forms of hate speech. The research urges the official religious authorities in Arab and Islamic countries to take on the legitimate, ethical, and scientific duty of freeing religious matters from ideological manipulation and restoring the correct approach to interpreting religious texts, while avoiding extremist ideological exploitation. This proposal advocates for the promotion of harmony, resolution of misunderstandings, fostering love and unity, prevention of excommunication, defamation, and conflict. It suggests the establishment of educational programs focused on promoting peace and coexistence values, as well as encouraging research in the field of tolerance education and acceptance of others. The objective is to cultivate an intellectual atmosphere in our universities that prioritizes wisdom, reason, logic, and evidence over emotional slogans. This will result in universities producing graduates who possess values of tolerance and coexistence, equipped to challenge and dismantle hateful and extremist ideologies by exposing their flaws and removing the religious facade from their harmful ideas.

Leveraging quantum uncertainty: Quantum randomness through the lens of classical communication networks

The generation of random numbers and the study of its properties have been an elusive field for a fair portion of the century. The application of random numbers is employed in many use cases such as cryptography, neural networks, numerical simulation, and gambling. The performance of each of these use cases is profoundly impacted by the employed random numbers; henceforth, the quality of randomness is of critical importance when it comes to their usage. A poorly generated random number can make a security system vulnerable, or any numerical or statistical evaluation misleading. Although various modes of classical random number generators exist and still function to provide strong cryptographic properties, emergence of quantum mechanical randomness has shed light on a novel path of generating certified randomness which supersedes the classical counterpart in terms of security. Harnessing quantum mechanical phenomena enables generation of true random numbers which can be certified and further implemented to elevate the net quality of the specific use cases. In this work, we generate and analyze random numbers from three different sources — 50: 50 beam splitter (BS), quantum key distribution (QKD) setup with classical post-processing scheme, and a commercially available quantum random number generator (QRNG) (ID Quantique (IDQ)). The quality of the generated random numbers from the various sources is checked in statistical tests and compared. Further on, we have developed a system which implements the QRNG-based random numbers to facilitate message authentication code (MAC) and one time password (OTP) protocols, demonstrating a communication network application. In this manner we discuss about a network which integrates quantum mechanics to the current classical networking approaches to enhance certain aspects of the networking protocol — in this case, the security.

Unveiling vacuum fluctuations and nonclassical states with cavity-enhanced tripartite interactions

Enhancing and tailoring light–matter interactions offer remarkable nonlinear resources with wide-ranging applications in various scientific disciplines. In this study, strong and deterministic tripartite “beamsplitter” (“squeeze”) interactions are constructed by utilizing cavity-enhanced nonlinear anti-Stokes (Stokes) scattering within spin–photon–phonon degrees of freedom. We explore exotic dynamical and steady-state properties associated with the confined motion of a single atom within a high-finesse optical cavity. Notably, we demonstrate the direct extraction of vacuum fluctuations of photons and phonons, which are inherent in Heisenberg’s uncertainty principle, without requiring any free parameters. Moreover, our approach enables the realization of high-quality single-quanta sources with large average photon (phonon) occupancies. The underlying physical mechanisms responsible for generating the nonclassical quantum emitters are attributed to the decay-enhanced single-quanta blockade and long-lived motional phonons, resulting in strong nonlinearity. This work unveils significant opportunities for hitherto studying unexplored physical phenomena and provides novel perspectives on fundamental physics dominated by strong tripartite interactions.

Number nativism1

AbstractNumber Nativism is the view that humans innately represent precise natural numbers. Despite a long and venerable history, it is often considered hopelessly out of touch with the empirical record. I argue that this is a mistake. After clarifying Number Nativism and distancing it from related conjectures, I distinguish three arguments which have been seen to refute the view. I argue that, while popular, two of these arguments miss the mark, and fail to place pressure on Number Nativism. Meanwhile, a third argument is best construed as a challenge: rather than refuting Number Nativism, it challenges its proponents to provide positive evidence for their thesis and show that this can be squared with apparent counterevidence. In response, I introduce psycholinguistic work on The Tolerance Principle (not yet considered in this context), propose that it is hard to make sense of without positing precise and innate representations of natural numbers, and argue that there is no obvious reason why these innate representations couldn't serve as a basis for mature numeric conception.

Extended uncertainty principle via Dirac quantization

Extended uncertainty principle via Dirac quantization

Sharper Hardy Uncertainty Relations on Signal Concentration in Terms of Linear Canonical Transform

Sharper Hardy Uncertainty Relations on Signal Concentration in Terms of Linear Canonical Transform

Metalens array for quantum random number

Quantum random number generation (QRNG) leveraging intrinsic quantum uncertainty has attracted significant interest in the field of integrated photonic architecture, with applications in quantum cryptography, tests of quantum nonlocality, and beyond. The demand for compact, low-energy consumption, robust, fast, and cost-effective QRNGs integrated into photonic chips is highlighted, whereas most previous works focused on bulk optics. Here, based on the metalens array entangled source, we experimentally realized a miniaturized, high-dimensional quantum random number generator via a meta-device without post-randomness extraction. Specifically, the device has a high-density output with 100 channels per square millimeter. This chip-scale quantum randomness source can obtain random number arrays without post-randomness extraction and enable compact integration for quantum applications needing secure keys or randomness. Our approach demonstrates potential in secure key generation and randomness for quantum applications.

Stability of the logarithmic Sobolev inequality and uncertainty principle for the Tsallis entropy

We consider the stability of the functional inequalities concerning the entropy functional. For the Boltzmann–Shannon entropy, the logarithmic Sobolev inequality holds as a lower bound of the entropy by the Fisher information, and the Heisenberg uncertainty principle follows from combining it with the Shannon inequality. The optimizer for these inequalities is the Gauss function, which is a fundamental solution to the heat equation. In the fields of statistical mechanics and information theory, the Tsallis entropy is known as a one-parameter extension of the Boltzmann–Shannon entropy, and the Wasserstein gradient flow of it corresponds to the quasilinear diffusion equation. We consider the improvement and stability of the optimizer for the logarithmic Sobolev inequality related to the Tsallis entropy. Furthermore, we show the stability results of the uncertainty principle concerning the Tsallis entropy.