Quantum correlation enhanced bound of the information exclusion principle

We investigate the information exclusion principle for multiple measurements with assistance of multiple quantum memories that are well bounded by the upper and lower bounds.The lower bound depends on the observables'complementarity and the complementarity of uncertainty whilst the upper bound includes the complementarity of the observables,quantum discord,and quantum condition entropy.In quantum measurement processing,there exists a relationship between the complementarity of uncertainty and the complementarity of information.In addition,based on the information exclusion principle the complementarity of uncertainty and the shareability of quantum discord can exist as an essential factor to enhance the bounds of each other in the presence of quantum memory.

Quantum uncertainty relations of quantum coherence and dynamics under amplitude damping channel

In this paper, we discuss quantum uncertainty relations of quantum coherence through a different method from Ref. [52]. Some lower bounds with parameters and their minimal bounds are obtained. Moreover, we find that for two pairs of measurement bases with the same maximum overlap, quantum uncertainty relations and lower bounds with parameters are different, but the minimal bounds are the same. In addition, we discuss the dynamics of quantum uncertainty relations of quantum coherence and their lower bounds under the amplitude damping channel（ADC）. We find that the ADC will change the uncertainty relations and their lower bounds, and their tendencies depend on the initial state.

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

We show that violation of the variance based local sum uncertainty relation(LSUR)for angular momentum operators of a bipartite system,proposed by Hofmann and Takeuchi[Phys.Rev.A 68032103(2003)],reflects entanglement in the equal bipartitions of an N-qubit symmetric state with even qubits.We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix[Phys.Lett.A 364203(2007)]of the two-qubit reduced system of a permutation symmetric N-qubit state.

Dose-Injury Relation as a Model for Uncertainty Propagation from Input Dose to Target Dose

We study a general framework for assessing the injury probability corresponding to an input dose quantity. In many applications, the true value of input dose may not be directly measurable. Instead, the input dose is estimated from measurable/controllable quantities via numerical simulations using assumed representative parameter values. We aim at developing a simple modeling framework for accommodating all uncertainties, including the discrepancy between the estimated input dose and the true input dose. We first interpret the widely used logistic dose-injury model as the result of dose propagation uncertainty from input dose to target dose at the active site for injury where the binary outcome is completely determined by the target dose. We specify the symmetric logistic dose-injury function using two shape parameters: the median injury dose and the 10 - 90 percentile width. We relate the two shape parameters of injury function to the mean and standard deviation of the dose propagation uncertainty. We find 1) a larger total uncertainty will spread more the dose-response function, increasing the 10 - 90 percentile width and 2) a systematic over-estimate of the input dose will shift the injury probability toward the right along the estimated input dose. This framework provides a way of revising an established injury model for a particular test population to predict the injury model for a new population with different distributions of parameters that affect the dose propagation and dose estimation. In addition to modeling dose propagation uncertainty, we propose a new 3-parameter model to include the skewness of injury function. The proposed 3-parameter function form is based on shifted log-normal distribution of dose propagation uncertainty and is approximately invariant when other uncertainties are added. The proposed 3-parameter function form provides a framework for extending skewed injury model from a test population to a target population in application.

Gravitational Space-Time Quantization for Charged Wormholes and the Diophantine Uncertainty Relation

This research work proceeds from the assumption, which was still considered by Einstein, that the quantization of gravity does not require additional external procedures: quantum phenomena can be a consequence of the properties of the universal gravitational interaction, which maps any physical field upon the space-time geometry. Therefore, an attempt is made in this research work to reduce the quantization of physical fields in GRT to the space-time quantization. Three reasons for quantum phenomena are considered: Partition of space-time into a set of unconnected Novikov’s R- and T-domains impenetrable for light paths;the set is generated by the invariance of Einstein’s equations with respect to dual mappings;The existence of electric charge quanta of wormholes, which geometrically describe elementary particles in GRT. This gives rise to a discrete spectrum of their physical and geometric parameters governed by Diophantine equations. It is shown that the fundamental constants (electric charge, rest masses of an electron and a proton) are interconnected arithmetically;The existence of the so-called Diophantine catastrophe, when fluctuations in the values of physical constants tending to zero lead to fluctuations in the number of electric charges and the number of nucleons at the wormhole throats, which tend to infinity, so that the product of the increments of these numbers by the increment of physical constants forms a relation equivalent to the uncertainty relation in quantum mechanics. This suggests that space-time cannot but fluctuate, and, moreover, its fluctuations are bounded from below, so that all processes become chaotic, and the observables become averaged over this chaos.

Uncertainty relations in the product form

We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy-Schwarz inequality.

Higher-order squeezing of quantum field and higher-order uncertainty relations in non-degenerate four-wave mixing

It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.

A Relational Sociological Study on the Effects of Uncertainties in the Case of Influenza in Turkey

Health issues, especially global health issues, are important subjects of study for many sociologists. For example, the spread of influenza as a pandemic affects a large number of people and their emotions in terms of fear, becoming a social problem instead of a psychological issue. Because of uncertainties, what is happening and what people should do during global threats is not clear for many people generally and during pandemics specifically. The primary aim of this paper is to show the construction process of fear and risk by conducting a systematic review of former studies about the influenza that occurred in Turkey during the last 10 years. It is assumed that a combination of relational sociology and the sociology of disaster and development will provide an appropriate theoretical framework. In other words, H. White and his uncertainty typology along with A.E. Collins’ classification are both used to define the construction process of fear as a culture, starting with uncertainty and moving to alienation and finally normalization. Findings from this study, which are supported by N. Elias’ and U. Beck’s methodological considerations, revealed that uncertainties may lead to negative consequences, such as alienation. Due to conflicting information, people find themselves in a dilemma and they stop following norms and rules in terms of normlessness. Normlessness, as a sub-division of alienation along with meaningless, might result in negative actions, such as not getting vaccinated. Liminality, turning points and footing are also used to describe the construction process of fear and risk. Results also showed that over a 10-year period many things are normalized and people no longer panic as easily.

Fine-grained uncertainty relation for open quantum system

The fine-grained uncertainty relation (FUR) is investigated for accelerating open quantum system, which manifests the celebrated Unruh effect, a crucial piece of the jigsaw for combining relativity and quantum physics. For a single detector, we show that the inevitable Unruh decoherence can induce a smaller FUR uncertainty bound, which indicates an additional measurement uncertainty may exist. For an open system combined with two detectors, via a nonlocal retrieval game, the related FUR uncertainty bound is determined by the non-classical correlation of the system. By estimating the maximal violation of Bell inequality for an accelerating system, we show that the FUR uncertainty bound can be protected from Unruh decoherence, due to quantum correlation generated through Markovian dynamics.

Quantum correlation and entropic uncertainty in a quantum-dot system

We explore the dynamical behaviors of the measurement uncertainty and quantum correlation for a vertical quantumdot system in the presence of magnetic field, including electron-electron interaction and Coulomb-blocked systems. Stemming from the quantum-memory-assisted entropic uncertainty relation, the uncertainty of interest is associated with temperature and parameters related to the magnetic field. Interestingly, the temperature has two kinds of influences on the variation of measurement uncertainty with respect to the magnetic-field-related parameters. We also discuss the relation between the lower bound of Berta et al. and the quantum discord. It is found that there is a natural competition between the quantum discord and the entropy min_(Π~B_(i)) SΠ~B_(i)(ρ_(A|B)). Finally, we bring in two improved bounds to offer a more precise limit to the entropic uncertainty.

Uncertainty Relations for Some Central Potentials in N-Dimensional Space

We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.

Formal Verification of Robertson-Type Uncertainty Relation

Formal verification using interactive theorem provers have been noticed as a method of verification of proofs that are too big for humans to check the validity of them. The purpose of this work is to verify the validity of Robertson-type uncertainty relation toward verifying unconditional security of quantum key distributions. We verify the validity of the relation by using proof assistant Coq and it is turned out that the theorem regarding the relation formally holds. The source code for Coq which represents the validity of the theorem is printed in Appendix.

Information Interpretation of Heisenberg Uncertainty Relation

In this paper the following information interpretation of uncertainty relation is proposed: if one bit of information was extracted from the system as a result of the measurement process, then the measurement itself adds an additional uncertainty (chaos) into the system equaled to one bit. This formulation is developed by calculating of the Shannon information entropy for the classical N-slit interference experiment. This approach allows looking differently at several quantum phenomena. Particularly, the information interpretation is used for explanation of entangled photons diffraction picture compression.

Generalized Uncertainty Relations, Curved Phase-Spaces and Quantum Gravity

Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.

Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants

Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties.For any quantum state,we establish optimal sets of three observables for both product and summation forms of uncertainty relations,and analytically derive the corresponding tightest uncertainty constants.We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form.Furthermore,the existence of the tightest constants excludes the validity of standard real quantum mechanics,underscoring the essential role of complex numbers in this field.Additionally,our findings resolve the conjecture posed in[Phys.Rev.Lett.118,180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.

Tighter sum uncertainty relations via(α,β,γ)weighted Wigner–Yanase–Dyson skew information

We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew information.The results are also applicable to the(α,γ)weighted Wigner–Yanase–Dyson((α,γ)WWYD)skew information and the weighted Wigner–Yanase–Dyson(WWYD)skew information.We also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner–Yanase–Dyson((α,β,γ)MWWYD)skew information.Detailed examples are provided to illustrate the tightness of our uncertainty relations.

Uncertain Relation Suited to Overfitting of BP Neural Network

A general uncertainty relation between the change of weighted value which represents learning ability and the discrimination error of unlearning sample sets which represents generalization ability is revealed in the modeling of back propagation (BP) neural network. Tests of numerical simulation for multitype of complicated functions are carried out to determine the value distribution (1×10?5~5×10?4) of overfitting parameter in the uncertainty relation. Based on the uncertainty relation, the overfitting in the training process of given sample sets using BP neural network can be judged.

The empirical relationships between M_S,m_band M_L for China and vicinity

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The Boltzmann Constant: Evaluation of Measurement Relative Uncertainty Using the Information Approach

The purpose of this work is to prove that only by applying a theoretically sound information approach to developing a model for measuring the Boltzmann constant, one can justify and calculate the value of the required relative uncertainty. A dimensionless parameter (comparative uncertainty) was proposed as a universal metric for comparing experimental measurements of Boltzmann constant and simulated data. Examples are given of applying the proposed original method for calculating the relative uncertainty in measuring the Boltzmann constant using an acoustic gas thermometer, dielectric constant gas thermometer, Johnson noise thermometer, Doppler broadening thermometer. The proposed approach is theoretically justified and devoid of the shortcomings inherent in the CODATA concept: a statistically significant trend, a cumulative value of consensus or a statistical control. We tried to show how a mathematical-expert formalism can be replaced by a simple, theoretically grounded postulate on the use of information theory in measurements.

Evaluation of Uncertainty for Determination of Stevioside Content in Fermented Milk by HPLC

[Objectives]The paper was to establish an evaluation method for the uncertainty of stevioside(including stevioside,rebaudioside A,rebaudioside B,rebaudioside C,rebaudioside F,Dulcoside A,rubusoside and steviolbioside)content determination in fermented milk based on HPLC.[Methods]The mathematical model of stevioside content and the propagation rate of uncertainty were established,and the sources of uncertainty were analyzed.[Results]The uncertainty mainly came from four main aspects,including standard uncertainty u(C)introduced by solution concentration C,standard uncertainty u(V)introduced by sample volume V,standard uncertainty u(m)introduced by sample mass m weighing and standard uncertainty u(f_(rep))introduced by measurement repeatability of stevioside content after sample dissolution and constant volume.The uncertainty estimation table and fishbone chart of stevioside content X determination were established.The relative synthetic standard uncertainty of stevioside content was obtained,and the standard uncertainty was extended to form the measurement result of stevioside content and its uncertainty report.[Conclusions]The evaluation results can be directly applied to the daily practical detection work.