Quantum Byzantine Agreement with Tripartite Entangled States

We present a quantum protocol for resolving the detectable Byzantine agreement (BA) problem using tripartite Greenberger–Horne–Zeilinger(GHZ)-like states and homodyne measurements in the continuous variable (CV) scenario. The protocol considers the simplest (i.e., three-player) BA problem involving one broadcaster and two receivers who jointly participant in the distribution, test, and agreement phases. The GHZ-like states provide the quantum resources for implementing the primitive of BA and satisfy a priori entanglement bound. Analyses demonstrate that the proposed quantum solution adheres to the agreement, validity, and termination criteria. Conveniently, the beam splitter strategy along with photon detection offers a method for comparing quantum messages. The paper shows that a potential high-efficiency CV-based BA protocol can be achieved using standard off-the-shelf components in quantum optics, maintaining the desirable characteristics of CVs when compared with discrete-variable BA protocol.

     

Experimental demonstration of a quantum protocol for byzantine agreement and liar detection

We introduce a new quantum protocol for solving detectable Byzantine agreement (also called detectable broadcast) between three parties, and also for solving the detectable liar detection problem. The protocol is suggested by the properties of a four-qubit entangled state, and the classical part of the protocol is simpler than that of previous proposals. In addition, we present an experimental implementation of the protocol using four-photon entanglement.     

A New Solution to Detectable Byzantine Agreement Problem

We present a new quantum protocol for solving detectable Byzantineagreement problem between three parties by employing one quantumkey distribution protocol. The protocol is suggested by a special four-qubit entangled state instead of singlet states, which shows that singlet states are not necessary to achieve detectable Byzantine agreement.     

A New Multi-Party Quantum Private Comparison Protocol Based on Circle Model

Recently multi-party quantum private comparison (MQPC) has attracted more and more attentions in the research of quantum cryptography. In our paper, a new MQPC protocol has been proposed by encoding the compared secrets on the phase of n-level single photons. From the proposed protocol, a generic model named circle model can be summarized. With the help of a semi-honest third party (TP), it can be proved that our protocol is immune to the outside attack and dishonest participants’ (including TP) attack.

     

Free Induction Signals after Multipulse Excitation of a Spin System

A free induction signal (FIS) after excitation of a two-level inhomogeneously broadened spin system by a sequence of n electromagnetic pulses of the same duration t ₁ and with the same intervals between them is investigated theoretically and experimentally. It has been established that an FIS develops n coherent oscillations of magnetization, whose phases change in time following definite laws. These oscillations arise after cessation of the nth pulse and terminate successively at times that are multiple of t ₁, thus increasing the FIS duration. The conclusion has been drawn on the validity of the theorem of coherent transient processes on multipulse excitation of two-level spin systems with a finite inhomogeneous line width. The theoretical results are in fairly good agreement with the experimental data obtained in the NMR of protons in glycerin.     

A (<Emphasis Type="Italic">t</Emphasis>,<Emphasis Type="Italic">n</Emphasis>)-Threshold Scheme of Multi-party Quantum Group Signature with Irregular Quantum Fourier Transform

A novel (t,n)-threshold scheme for the multi-party quantum group signature is proposed based on the irregular quantum Fourier transform, in which every t-qubit quantum message needs n participants to generate the quantum group signature. All the quantum operation gates in the quantum circuit can be distributed and arranged randomly in the irregular QFT algorithm, which can increase the von Neumann entropy of the signed quantum message and the randomicity of the quantum signature generation significantly. The generation and verification of the quantum group signature can be both performed in quantum circuits with the parallel algorithm. Security analysis shows that an available and legal quantum (t,n)-threshold group signature can be achieved.     

Linear and angular velocity autocorrelation functions for two-dimensional systems of repulsive and Lennard-Jones diatomics

The method of molecular dynamics has been employed to study the autocorrelation functions (ACF's) of the linear velocity and of the angular momentum for two two-dimensional systems of diatomic molecules. The anisotropic potential used is built from four atom-atom interactions. These are either purely repulsive (R), or repulso-attractive (LJ). Emphasis has been put on the long-time behaviour; for this we have used large systems (1600 molecules). The density lies in the intermediate range.

The linear velocity ACF exhibits, for system R, an initial decay which is exponential and whose characteristic time has been checked to be of the order of the mean ‘collision’ time. For system LJ (where collisions cannot be usefully defined) the decay does not follow a simple law, and lies above a single exponential. After an intermediate regime which lasts a long time-span for both systems, the ACF's adopt a t ^-1 decay in agreement with theoretical predictions based on hydrodynamics or other approaches.

The mean square displacement has also been extracted from the data. Its ratio to time, i.e. the apparent coefficient of diffusion, increases logarithmically with time, so that the two kinds of data are in accord. This asymptotic regime starts after about 11 collision times for the repulsive system, and about as soon for the other one.

The angular momentum ACF's, after an initial decay which is closer to an exponential for system R than for system LJ, adopt a t ^-3 behaviour for a very long time-span; this possibly masks a final t ^-2 decay predicted by several theories based on the coupling of the intrinsic momentum with the vorticity of the fluid.     

Vibrational analysis of nitrosamine,a molecule with an almost constant potential along the inversion coordinate

ABSTRACT

The fundamental vibrational transitions of nitrosamine and its doubly deuterated isotopologue have been computed by vibrational configuration interaction theory including up to 6-tuple excitations. The potential energy surface has been represented by an n-mode expansion up to 4-mode couplings terms obtained from explicitly correlated coupled-cluster theory, CCSD(T)-F12a. Very good agreement with experimental data has been been achieved and a number of new assignments is provided.     

Emission of light nuclei (<Emphasis Type="Italic">p,d, t</Emphasis>, α) in the process of annihilation of slow antiprotons in nuclear emulsion

The annihilation of slow (∼7 MeV) antiprotons in nuclear emulsion has been studied. The yields and energy spectra of p, d, t, and α particles in the evaporation region have been measured. The shape of the spectra of p, d, and t is in agreement with the Maxwell distribution and the excitation energy of a nucleus is consistent with a theoretical estimate for evaporation from the equilibrium state. The probability of the absorption of antiprotons inside the nucleus estimated from the multiplicity of h particles is ɛ = (2.0 ± 0.6) × 10⁻². The relative d/p yield coincides with a similar ratio appearing in the capture of slow π⁻ mesons by nuclei in the nuclear emulsion. The yields of t and α particles in the process of the annihilation of antiprotons are much higher than those in a similar process for pions. To identify g particles (0.29 < β < 0.70), energy losses dE/dx on ionization and multiple scattering have been measured. In this velocity region, the yields of p, d, t, and pions have been observed. The ratios (n _d /n _p ) _g , (n _d /n _p ) _b , and n _d /n _p measured in the capture of π⁻ mesons are almost the same. In this velocity range (g particles), α particles have not been observed.     

Member expansion in quantum (t,n) threshold secret sharing schemes

A protocol for member expansion in quantum (t,n) threshold secret sharing schemes was proposed. Without a trusted center and modifying the shares of old participants, the protocol needs that t (t is the threshold) old participants cooperate to generate the new share. Compared with the previous secret sharing protocols, the proposed protocol has the advantage of joining new participants agilely.     

Nonexponential Photoluminescence Dynamics in an Inhomogeneous Ensemble of Excitons in WSe2 Monolayers

The spectral and spatiotemporal dynamics of photoluminescence in monolayers of transition metal dichalcogenide WSe₂ obtained by mechanical exfoliation on a Si/SiO₂ substrate is studied over a wide range of temperatures and excitation powers. It is shown that the dynamics is nonexponential and, for times t exceeding ∼50 ps after the excitation pulse, is described by a dependence of the form 1/(t + t₀). Photoluminescence decay is accelerated with a decrease in the temperature and in the energy of emitting states. It is shown that the observed dynamics cannot be described by a bimolecular recombination process, such as exciton—exciton annihilation. A model that describes the nonexponential photoluminescence dynamics by taking into account the spread of radiative recombination times of localized exciton states in a random potential gives good agreement with experimental data.

     

Thermal Cross‐Linking of Poly(Vinyl Methyl Ether). II. Rheological Behavior at the Gel Point

Abstract

Isothermal time evolution measurements at different constant temperatures (170°C, 180°C, and 190°C) over a wide range of frequency for the thermal cross‐linking process of poly(vinyl methyl ether), PVME, have been investigated rheologically. At the onset of cross‐linking (t _onset) the elastic storage modulus, G′, increases abruptly. The magnitude of the elevation in G′ and the value of t _onset were found to be temperature‐dependent. Similar behavior was observed for both the viscous loss modulus, G″ and the complex dynamic viscosity, η*; however, the value of G″ shows a very low sensitivity to the cross‐linking process compared to G′ and η* at the same experimental conditions. The gel point, t _gel, was evaluated from the point of intersection in plots of tan δ vs. curing time for different constant shear frequencies. At the gel point tan δ is no longer frequency‐dependent, and all curves cross‐over, indicating the validity of the Winter–Chambon criterion. The value of t _gel obtained from the coincidence of G′ and G″ was about 10 min longer than that determined from tan δ vs. t, indicating that the crossover of G′ and G″ is not be considered as a general method for evaluation of t _gel. The value of the apparent activation energy of gelation determined from the temperature dependence of t _gel was 74 kJ mol^?1 in good agreement with literature values for other different systems. At the gel point G′ and G″ showed a power law with shear frequency, i.e., G′ ～ G″ ～ ω _n with critical exponents equal to 0.64 and 0.75, respectively, in close agreement with the percolation theory (n = 2/3). The zero shear viscosity, η₀, and the equilibrium shear modulus, G _eq, can also be expressed in power low scaling functions with the relative distance from the gel point, ? i.e., η₀ ～ ?^?k and G _eq ～ ? ^z with k = 1.3 and z = 2.4 in good agreement with the predicted values based on the percolation theory.     

Simultaneous Measurement of Refractive Index and Thickness by Low Coherence Interferometry Considering Chromatic Dispersion of Index

Low coherence interferometry can provide simultaneous measurement of refractive index n and thickness t of a transparent plate, as reported recently by some research groups. Precise measurement of n and t is impossible unless chromatic dispersion of index is taken into account. We then proposed and demonstrated a unique technique for simultaneous measurement of phase index n_p, group index n_g and thickness t using a special sample holder. This paper describes a novel technique for simultaneous measurement of n_p, n_g and t using an approximate expression of the chromatic dispersion in terms of n_p. The approximate expression of chromatic dispersion does not require use of the special sample holder, and n_p, n_g and t are determined from two measurable quantities with an accuracy of 0.3% or less, for the sample thickness was around 1 mm. In addition, it is possible to shorten the measurement time compared with the above method.     

Computation and analysis of the dynamic structure factor S(k, ω) for small wave vectors

Molecular dynamics (MD) calculations have been performed for the Lennard-Jones (12-6) potential function using 2048 particles. Using conventional parameters the results may be compared with those for liquid argon.

The dynamic structure factor S(k, ω) has been determined both by Fourier inversion of the intermediate scattering function F(k, t) and from the longitudinal current-current correlation function C _∥(k, t). Particular attention was paid to the recurrence time of the system. The results for S(k, ω) by the two methods agree within 5 per cent for the whole region of small k-vectors considered. Double Fourier inversion of the van Hove function G(r, t) led to insufficiently accurate results for these small k-values. In view of the present data, the MD-results of Levesque et al. [1] for S(k, ω) have only a qualitative character. These latter data appear to contain truncation errors due to incomplete Fourier transformations.

Using a hydrodynamic assumption for F(k, t) we were able to extract the transport coefficients, the velocity of sound and the ratio of the specific heats in the limit of large wave lengths or small k. The velocity of sound was obtained by exploiting the MD generated anomalous dispersion curve of sound waves. Anomalous dispersion was found to set in for kσ ～ 0·25. A sound speed of 880 ms^-1 has been determined which is in excellent agreement with experimental values for liquid argon. The total error for the MD value amounts to about 5 per cent. In contrast, the ratio of the specific heats γ and the transport coefficients D _T and Γ (thermal diffusivity and sound attenuation) were determinable only with an accuracy of 15 per cent due to the need for larger extrapolations. Nevertheless, we found D _T, Γ and γ in agreement with experimental values within 5-10 per cent.     

The effect of preionization electron number density on avalanche completion time

Laser output of discharge excimer lasers is related to the avalanche completion timet _A. The important role of preionization electron number densityn _e(0) in reducingt _A is then considered. A simple two-stage model is proposed to describe the electron avalanche process under marginalE/n conditions. The theoretical predictions according to the two stage model are in good agreement with the experiments. That vigorous preionization is critical to stable operation of large aperture, high pressure discharge devices is concluded.A portion of the work was done when the author was at UCSD     

Exact probability distributions for noncorrelated random walk models

A stochastic model for the idealized locomotion of cells is studied. The cell is assumed to cover a polygonal line in ⁿ , the times between turns are exponentially distributed and independent of the directions, and the density of thenth directione does not depend on the (n–1)th directione. The resulting Markov process (X(t), D(t)) for position and direction of the motion at timet is studied by using the integrodifferential equation for the transition function. For example, the joint distribution of (X(t), D(t)) is derived in closed form ifn=2 orn=3 and all chosen directions (including the initial one) are uniformly distributed. For higher dimensions the combined Fourier-Laplace transform ofX(t) is given. The case of a fixed initial direction is also considered.     

Impurity bands in a magnetic field of arbitrary strength

On the basis of the self-consistentt-matrix approximation for a system of quasi free electrons interacting with randomly distributed attractive-potentials, we discuss impurity bands in the presence of a magnetic field of arbitrary strength. We compare the results with existing theoretical work on the limiting cases of weak and strong magnetic fields, which are shown to be partly incompatible, and with experimental work onn-type InSb in the magnetic freeze-out regime. Satisfactory agreement is obtained between the thermal ionisation energy, evaluated from experiments, and the calculated gap energy, separating impurity band and conduction band.     

Factorization and Dilation Problems for Completely Positive Maps on von Neumann Algebras

We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism groups. The starting point for our investigation has been the question of existence of non-factorizable Markov maps, as formulated by C. Anantharaman-Delaroche. We provide simple examples of non-factorizable Markov maps on M_n(\mathbbC){M_n(\mathbb{C})} for all n ≥ 3, as well as an example of a one-parameter semigroup (T(t)) _t≥0 of Markov maps on M₄(\mathbbC){M_4(\mathbb{C})} such that T(t) fails to be factorizable for all small values of t > 0. As applications, we solve in the negative an open problem in quantum information theory concerning an asymptotic version of the quantum Birkhoff conjecture, as well as we sharpen the existing lower bound estimate for the best constant in the noncommutative little Grothendieck inequality.     

Critical dynamics and stability of elastically coupled systems at marginal dimensionalities

Static and dynamic behavior of an-component classical model atd=4 has been investigated assuming a coupling to a fluctuating lattice displacement field. Solutions of renormalization-group (RG) equations are given for elastically isotropic and anisotropic systems, and the temperature dependences of elastic constants and of the corresponding damping coefficients are calculated. For isotropic and weakly anisotropic systems it is found that forn<4 the critical regime can be split into a rigid regimet>t _s , and a compressible regimet<t _s , wheret=(T–T _c )/T _c andt _s is a crossover temperature. In the rigid regime, the logarithmic correction factors characterizing deviations from Landau theory have the same form as in systems without elastic coupling; in the compressible regime the exponents are renormalized by the coupling. Forn4 rigid behavior prevails at all temperatures; similarly only rigid behavior is found for strongly anisotropic systems for alln. The thermodynamic stability of the system is investigated by evaluating the contribution of ring diagrams for the casen=1. It is thus shown that under constant hydrostatic pressure a first-order transition occurs in both isotropic and anisotropic systems, and the corresponding equations for the transition temperature and the value of the order parameter atT _c are derived.     

Optical properties of low-dimensional organic conductors with differently oriented conducting layers: (EDT-TTF)3Hg2Br6 and (EDT-TTF)3Hg(SCN)3I0.5(PhCl)0.5

Spectral optical investigations of two low-dimensional organic molecular conductors with differently oriented conducting layers of ethylenedithiotetrathiafulvalene (EDT-TTF) molecules, namely, the (EDT-TTF)₃Hg₂Br₆ and (EDT-TTF)₃Hg(SCN)₃I_0.5(PhCl)_0.5 single crystals, have been carried out. The polarized reflectance spectra of the single crystals have been measured in the frequency range 700–6500 cm⁻¹ (0.087–0.810 eV) at temperatures from 300 to 15 K. The optical conductivity spectra have been obtained using the Kramers-Kronig relations, and their quantitative analysis has been performed in terms of a theoretical model that takes into account electron-electron correlations in the approximation of the Hubbard Hamiltonian for trimerized stacks, the vibronic coupling, and the influence of the counterion on the electronic states in the trimer. A satisfactory agreement between the theoretical and experimental spectra for both crystals made it possible to estimate the parameters of the electronic structure of the crystals in the conducting plane: the integral t of the electron transfer between the EDT-TTF molecules in the trimer, the energy U of the Coulomb repulsion between two electrons (holes) in one EDT-TTF molecule, the electron transfer damping constant γ _e , the energy shift Δ of the molecular orbital under the influence of the anions and vibronic coupling, the vibronic coupling constant g _n , and the binding energy E _p of the molecular polaron. It has been found that there are large differences in the anisotropies of the optical properties and the obtained Hubbard parameters of the electronic structure for the studied crystals.