Finite-size analysis of continuous-variable quantum key distribution with entanglement in the middle

Continuous-variable quantum key distribution(CVQKD) protocols with entanglement in the middle(EM) enable long maximal transmission distances for quantum communications. For the security analysis of the protocols, it is usually assumed that Eve performs collective Gaussian attacks and there is a lack of finite-size analysis of the protocols. However,in this paper we consider the finite-size regime of the EM-based CVQKD protocols by exposing the protocol to collective attacks and coherent attacks. We differentiate between the collective attacks and the coherent attacks while comparing asymptotic key rate and the key rate in the finite-size scenarios. Moreover, both symmetric and asymmetric configurations are collated in a contrastive analysis. As expected, the derived results in the finite-size scenarios are less useful than those acquired in the asymptotic regime. Nevertheless, we find that CVQKD with entanglement in the middle is capable of providing fully secure secret keys taking the finite-size effects into account with transmission distances of more than 30 km.

Assessment of force models on finite-sized particles at finite Reynolds numbers

Finite-sized inertial spherical particles are fully-resolved with the immersed boundary projection method(IBPM)in the turbulent open-channel flow by direct numerical simulation(DNS).The accuracy of the particle surface force models is investigated in comparison with the total force obtained via the fully-resolved method.The results show that the steady-state resistance only performs well in the streamwise direction,while the fluid acceleration force,the added-mass force,and the shear-induced Saffman lift can effectively compensate for the large-amplitude and high-frequency characteristics of the particle surface forces,especially for the wall-normal and spanwise components.The modified steady-state resistance with the correction effects of the acceleration and the fluid shear can better represent the overall forces imposed on the particles,and it is a preferable choice of the surface force model in the Lagrangian point-particle method.

Effects of finite-size neutrally buoyant particles on the turbulent channel flow at a Reynolds number of 395

A direct-forcing fictitious domain(DFFD) method is used to perform fully resolved numerical simulations of turbulent channel flows laden with large neutrally buoyant particles. The effects of the particles on the turbulence(including the mean velocity,the root mean square(RMS) of the velocity fluctuation, the probability density function(PDF) of the velocity, and the vortex structures) at a friction Reynolds number of 395 are investigated. The results show that the drag-reduction effect caused by finite-size spherical particles at low particle volumes is negligibly small. The particle effects on the RMS velocities at Re_τ = 395 are significantly smaller than those at Re_τ = 180, despite qualitatively the same effects, i.e., the presence of particles decreases the maximum streamwise RMS velocity near the wall via weakening the large-scale streamwise vortices,and increases the transverse and spanwise RMS velocities in the vicinity of the wall by inducing smaller-scale vortices. The effects of the particles on the PDFs of the fluid fluctuating velocities normalized with the RMS velocities are small, regardless of the particle size, the particle volume fraction, and the Reynolds number.

Influences of finite-size effects on the self-organized critical-ity of forest-fire model

The influences of finite-size effects on the self-organized criticality (SOC) of the traditional forest-fire model are investigated by means of a new method. The forest size is originally set to a value much greater than the correla-tion length of the forest. Finite-size effects are then studied by equally dividing the forest into more and more separate subsystems on condition that the forest size, igniting prob-ability and planting probability are invariant. A new phe-nomenon, i.e. the finite-size effects with one-side frequency peak, is observed. The boundary between two neighboring subsystems can be regarded as a firebreak. The concept of ’separation ability’ is introduced to represent the probability for the firebreak to block off the fire successfully. Restrain-ing effects of separation ability on finite-size effects are ana-lyzed. Finite-size effects and separation ability, as well as their relations are found to have practical importance to the actual forest-fire protection.

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|^(-(d-2+η))and a finite-size scaling function of the variables r/L and tL^(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.

Size effect on light propagation modulation near band edges in one-dimensional periodic structures

Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attracted wide attention.However,the practically fabricated structures can only have finite size,i.e.,limited numbers of periods,leading to changes of the light propagation modulation compared with infinite structures.Here,we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures.Near edges of the band gap,as the structure's size shrinks,the broadening of the band gap and the weakening of the light localization are discovered.When the size is small,an added layer on the surface will perform large modulation in the group velocity.Near the degenerate point with Dirac-like dispersion,the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes,while absolute group velocity fluctuates when the size shrinks.

Improving source-in-the-middle continuous-variable quantum key distribution using a heralded hybrid linear amplifier

A hybrid linear amplifier is inserted at the output of the source-in-the-middle distribution protocol to overcome the shortcomings of the transmission distance.The modified protocol aims to maintain a high key rate for long-distance transmission under high noise.It has the potential to significantly broaden the application range of the continuous variable quantum key distribution protocol.The effects of amplifier parameters and noise on the modified protocol are analyzed in detail with regard to applying it to a practical system.To make the simulation more realistic,the effect of finite size on the new protocol is taken into account.It will serve as a guideline for the future use of hybrid linear amplifiers.Different parameters can be adjusted to achieve the best performance for key rates of different quantum channels.

Continuum percolation of porous media via random packing of overlapping cube-like particles

The pore configuration in porous medium is assumed to be the randomly distributed cube-like particles which can overlap each other in the periodic cubic domain, and the impact of particle characteristics on the percolation property of these cube-like particle packing systems is analyzed.Firstly, by combining the percolation models and finite-size scaling analysis, three numerical parameters(i.e., percolation transition width △L, local percolation threshold ψ_c(L), and correlation length exponent v) for the cube-like particle systems with shape parameter s in[1.0, +∞] are derived successively. Then, based on the relation between the percolation thresholdψ_c in infinite space and the local percolation threshold ψ_c(L), the corresponding ψ_c with s in[1.0, +∞] are further determined. It is shown from the study that the characteristics of cube-like particles have significant influence on the global percolation threshold ψ_c of the particle packing systems. As the parameter s increases from 1.0 to +∞, the percolation threshold ψ_c will go down persistently. When the surface of cube-like particles is cubical and spherical, respectively, the minimum and maximum thresholds ψ_c,min and ψ_c,max are obtained.

Three-party reference frame independent quantum key distribution protocol

We present a three-party reference frame independent quantum key distribution protocol which can be implemented without any alignment of reference frames between the sender and the receiver.The protocol exploits entangled states to establish a secret key among three communicating parties.We derive the asymptotic key rate for the proposed protocol against collective attacks and perform a finite-size key security analysis against general attacks in the presence of statistical fluctuations.We investigate the impact of reference frame misalignment on the stability of our protocol,and we obtain a transmission distance of 180 km,200 km,and 230 km for rotation of reference framesβ=π/6,β=π/8 andβ=0,respectively.Remarkably,our results demonstrate that our proposed protocol is not heavily affected by an increase in misalignment of reference frames as the achievable transmission distances are still comparable to the case where there is no misalignment in reference frames(whenβ=0).We also simulate the performance of our protocol for a fixed number of signals.Our results demonstrate that the protocol can achieve an effective key generation rate over a transmission distance of about 120 km with realistic 107 finite data signals and approximately achieve 195 km with 109 signals.Moreover,our proposed protocol is robust against noise in the quantum channel and achieves a threshold error rate of 22.7%.

Optical responses of metallic plasmonic arrays under the localized excitation

The metallic plasmonic array that can support both propagating surface plasmon polaritons(PSPPs)and localized surface plasmon resonance(LSPR)possesses rich optical properties and remarkable optical performance,making it a powerful platform for applications in photonics,chemistry,and materials.For practical applications,the excitation spot is usually smaller than the area of metal arrays.It is thus imperative to address“how many array units are enough?”towards a rational design of plasmonic nanostructures.Herein,we employed focused ion beam(FIB)to precisely fabricate a series of plasmonic array structures with increased unit number.By utilizing photoluminescence(PL)and surface-enhanced Raman spectroscopy(SERS),we found that the array units outside the excitation spot still have a significant impact on the optical response within the spot.Combined with the numerical simulation,we found that the boundary of the finite array leads to the loss of PSPP outside the excitation point,which subsequently affects the coupling of PSPP and LSPR in the excitation spot,leading to variations in PL and SERS intensity.Based on the findings,we further tuned the LSPR mode of the metal arrays by electrodeposition to obtain strong near-field enhancement without any influence on the PSPP mode.This work advances the understanding of near-field and far-field optical behavior in finite-size array structures and provides guidance for designing highly-efficient photonic devices.

Experimental quantum secret sharing based on phase encoding of coherent states

Quantum secret sharing(QSS)is one of the basic communication primitives in future quantum networks which addresses part of the basic cryptographic tasks of multiparty communication and computation.Nevertheless,it is a challenge to provide a practical QSS protocol with security against general attacks.A QSS protocol that balances security and practicality is still lacking.Here,we propose a QSS protocol with simple phase encoding of coherent states among three parties.Removing the requirement of impractical entangled resources and the need for phase randomization,our protocol can be implemented with accessible technology.We provide the finite-key analysis against coherent attacks and implement a proof-of-principle experiment to demonstrate our scheme’s feasibility.Our scheme achieves a key rate of 85.3 bps under a 35 d B channel loss.Combined with security against general attacks and accessible technology,our protocol is a promising candidate for practical multiparty quantum communication networks.

Topological Landau–Zener nanophotonic circuits

Topological edge states(TESs),arising from topologically nontrivial phases,provide a powerful toolkit for the architecture design of photonic integrated circuits,since they are highly robust and strongly localized at the boundaries of topological insulators.It is highly desirable to be able to control TES transport in photonic implementations.Enhancing the coupling between the TESs in a finite-size optical lattice is capable of exchanging light energy between the boundaries of a topological lattice,hence facilitating the flexible control of TES transport.However,existing strategies have paid little attention to enhancing the coupling effects between the TESs through the finite-size effect.Here,we establish a bridge linking the interaction between the TESs in a finite-size optical lattice using the Landau–Zener model so as to provide an alternative way to modulate/control the transport of topological modes.We experimentally demonstrate an edge-to-edge topological transport with high efficiency at telecommunication wavelengths in silicon waveguide lattices.Our results may power up various potential applications for integrated topological photonics.

Condensation of eigen microstate in statistical ensemble and phase transition

In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.

Double Exchange Model in Triangular Lattice Studied by Truncated Polynomial Expansion Method

The low temperature properties of double exchange model in triangular lattice are investigated via truncated polynomial expansion method(TPEM),which reduces the computational complexity and enables parallel computation.We found that for the half-filling case a stable 120◦spin configuration phase occurs owing to the frustration of triangular lattice and is further stabilized by antiferromagnetic(AF)superexchange interaction,while a transition between a stable ferromagnetic(FM)phase and a unique flux phase with small finite-size effect is induced by AF superexchange interaction for the quarter-filling case.

Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model

The singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536.Fits of two data sets,one corresponding to certain value of the Binder cumulant and the other-to the maximum of CV,provide consistent values of C0 in the ansatz CV(L)=C0+AL^(a/n) at large L,if a/n=0.196(6).However,a direct estimation from our Cmax V data suggests that a/n,most probably,has a smaller value(e.g.,a/n=0.113(30)).Thus,the conventional power-law scaling ansatz can be questioned because of this inconsistency.We have found that the data are well described by certain logarithmic ansatz.

Evaluation of Three Lattice Boltzmann Models for Particulate Flows

A comparative study is conducted to evaluate three types of lattice Boltzmann equation(LBE)models for fluid flows with finite-sized particles,including the lattice Bhatnagar-Gross-Krook(BGK)model,the model proposed by Ladd[Ladd AJC,J.Fluid Mech.,271,285-310(1994);Ladd AJC,J.Fluid Mech.,271,311-339(1994)],and the multiple-relaxation-time(MRT)model.The sedimentation of a circular particle in a two-dimensional infinite channel under gravity is used as the first test problem.The numerical results of the three LBE schemes are compared with the theoretical results and existing data.It is found that all of the three LBE schemes yield reasonable results in general,although the BGK scheme and Ladd’s scheme give some deviations in some cases.Our results also show that the MRT scheme can achieve a better numerical stability than the other two schemes.Regarding the computational efficiency,it is found that the BGK scheme is the most superior one,while the other two schemes are nearly identical.We also observe that the MRT scheme can unequivocally reduce the viscosity dependence of the wall correction factor in the simulations,which reveals the superior robustness of the MRT scheme.The superiority of the MRT scheme over the other two schemes is also confirmed by the simulation of the sedimentation of an elliptical particle.