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.

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.

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.

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.

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.

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.

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.

Uncertainty relations for triples of observables and the experimental demonstrations

Uncertainty relations are of profound significance in quantum mechanics and quantum information theory.The well-known Heisenberg-Robertson uncertainty relation presents the constraints on the spread of measurement outcomes caused by the non-commutability of a pair of observables.In this article,we study the uncertainty relation of triple observables to explore the relationship between the standard deviations and the commutators of the observables.We derive and tighten the multiplicative form and weighted summation form uncertainty relations,which are found to be dependent not only on the commutation relations of each pair of the observables but also on a newly defined commutator in terms of all the three observables.We experimentally test the uncertainty relations in a linear optical setup.The experimental and numerical results agree well and show that the uncer-tainty relations derived by us successfully present tight lower bounds in the cases of high-dimensional observables and the cases of mixed states.Our method of deriving the uncertainty relation can be extended to more than three observables.

Uncertainty relations for general phase spaces

We describe a setup for obtain!ing uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the eciuality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.

Uncertainty Relations for Coherence

Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables.In terms of the coherence measure based on the Wigner-Yanase skew information,we establish several uncertainty relations for coherence with respect to von Neumann measurements,mutually unbiased bases(MUBs),and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively.Since coherence is intimately connected with quantum uncertainties,the obtained uncertainty relations are of intrinsically quantum nature,in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties).From a dual viewpoint,we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement.In particular,it is shown that if the density operators representing the quantum states do not commute,then there is no measurement(reference basis)such that the coherence of these states can be simultaneously small.

Uncertainty relations based on Wigner-Yanase skew information

In this paper,we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information.First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds.We then propose new weighted uncertainty relations for two noncompatible observables.Two separable criteria via skew information are also obtained.

Uncertainty relations based on skew information with quantum memory

Uncertainty principle is one of the most fascinating features of the quantum world.It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle,such as position and momentum,can not be simultaneously known.The uncertainty principle has attracted considerable attention since the innovation of quantum mechanics and has been investigated in terms of various types of uncertainty inequalities:in terms of the noise and disturbance,according to successive measurements,as informational recourses in entropic terms,by means of

Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.

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.

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.

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.

A newfangled study using risk silhouette and uncertainty approximation for quantification of acyclovir in diverse formulation

Risk assessment and uncertainty approximation are two major and important parameters that need to be adopted for the development of pharmaceutical process to ensure reliable results.Additionally,there is a need to switch from the traditional method validation checklist to provide a high level of assurance of method reliability to measure quality attribute of a drug product.In the present work,evaluation of risk profile,combined standard uncertainty and expanded uncertainty in the analysis of acyclovir were studied.Uncertainty was calculated using cause-effect approach,and to make it more accurately applicable a method was validated in our laboratory as per the ICH guidelines.While assessing the results of validation,the calibration model was justified by the lack of fit and Levene＇s test.Risk profile represents the future applications of this method.In uncertainty the major contribution is due to sample concentration and mass.This work demonstrates the application of theoretical concepts of calibration model tests,relative bias,risk profile and uncertainty in routine methods used for analysis in pharmaceutical field.

Reduction of entropic uncertainty in entangled qubits system by local PT-symmetric operation

We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with PT-symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local PT-symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian PT-symmetric operation.

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.