Finite-size Analysis Research Articles

Side-channel free quantum digital signature with source monitoring

Abstract Quantum digital signature (QDS) can guarantee the information-theoretical security of a signature with the fundamental laws of quantum physics. However, most current QDS protocols do not take source security into account, leading to an overestimation of the signature rate. In this paper, we propose to utilize Hong-Ou-Mandel interference to characterize the upper-bound of the source imperfections, and further to quantify information leakage from potential side-channels. Additionally, we combine decoy-state methods and finite-size analysis in analyzing the signature rate. Simulation results demonstrate the performance and feasibility of our approach. Our current work can improve the practical security of QDS systems, thereby promoting their further networked applications.

Finite-Resource Performance of Small-Satellite-Based Quantum-Key-Distribution Missions

In satellite-based quantum-key-distribution (QKD), the number of secret bits that can be generated in a single satellite pass over the ground station is severely restricted by the pass duration and the free-space optical channel loss. High channel loss may decrease the signal-to-noise ratio due to background noise, reduce the number of generated raw key bits, and increase the quantum bit error rate (QBER), all of which have detrimental effects on the output secret key length. Under finite-size security analysis, a higher QBER increases the minimum raw key length necessary for nonzero secret-key-length extraction due to less efficient reconciliation and postprocessing overheads. We show that recent developments in finite-key analysis allow three different small-satellite-based QKD projects, CQT-Sat, the United Kingdom QUARC-ROKS, and QEYSSat, to produce secret keys even under conditions of very high loss, improving on estimates based on previous finite-key bounds. This suggests that satellites in low Earth orbit can satisfy finite-size security requirements but that this remains challenging for satellites further from Earth. We analyze the performance of each mission to provide an informed route toward improving the performance of small-satellite QKD missions. We highlight the short- and long-term perspectives on the challenges and potential future developments in small-satellite-based QKD and quantum networks. In particular, we discuss some of the experimental and theoretical bottlenecks and the improvements necessary to achieve QKD and wider quantum networking capabilities in daylight and at different altitudes. Published by the American Physical Society 2024

Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions.

The fidelity is widely used to detect quantum phase transitions, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity F(γ,γ[over ̃]) always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states (γ and γ[over ̃]) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zeros of fidelity can be always accessed by tuning the magnetic flux when γ and γ[over ̃] belong to different phases. On the other hand, no exact zero of fidelity can be observed if γ and γ[over ̃] are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model, and Haldane model. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.

Critical behaviours of anisotropic XY ferromagnet in the presence of random field

The anisotropic XY ferromagnet has been studied by Monte Carlo simulation in a three dimensional simple cubic lattice. The increase in critical temperature (ferro-para transition) has been noticed with increasing the strength of anisotropy. The effects of random fields (both with full circular symmetry and in angular window) on the critical temperature are investigated systematically in the anisotropic XY ferromagnet in three dimensions. Reduction of the critical temperature of anisotropic XY ferromagnet has been observed in the presence of random field. The compensating field (the required amount of field which preserves the critical temperature for isotropic XY ferromagnet) has been studied as a function of the strength of anisotropy. The compensating field was found to depend linearly on the strength of anisotropy. We have also studied the effects of random field confined in the angular window and observed the reduction of the critical temperature with increase of the angular extension. The critical behaviours are formalised by the usual finite size analysis and the estimation of critical exponents for the susceptibility and the specific heat.

Blume-Capel model analysis with a microcanonical population annealing method.

We present a modification of the Rose-Machta algorithm [N. Rose and J. Machta, Phys. Rev. E 100, 063304 (2019)2470-004510.1103/PhysRevE.100.063304] and estimate the density of states for a two-dimensional Blume-Capel model, simulating 10^{5} replicas in parallel for each set of parameters. We perform a finite-size analysis of the specific heat and Binder cumulant, determine the critical temperature along the critical line, and evaluate the critical exponents. The obtained results are in good agreement with those previously obtained using various methods-Markov chain Monte Carlo simulation, Wang-Landau simulation, transfer matrix, and series expansion. The simulation results clearly illustrate the typical behavior of specific heat along the critical lines and through the tricritical point.

Absence of localization in weakly interacting Floquet circuits

We present a family of Floquet circuits that can interpolate between noninteracting qubits, free propagation, generic interacting, and dual-unitary dynamics. We identify the operator entanglement entropy of the two-qubit gate as a good quantitative measure of the interaction strength. We test the persistence of localization in the vicinity of the noninteracting point by probing spectral statistics, decay of autocorrelators, and measuring entanglement growth. The finite-size analysis suggests that the many-body localized regime does not persist in the thermodynamic limit. Instead, our results are compatible with an integrability-breaking phenomenon. Published by the American Physical Society 2024

Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways

We study the nonequilibrium phase transitions from the absorbing phase to the active phase for the model of diseases spreading (Susceptible-Infected-Refractory-Susceptible (SIRS)) on a regular one-dimensional lattice. In this model, particles of three species (S, I, and R) on a lattice react as follows: S+I→2I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S+I\\rightarrow 2I$$\\end{document} with probability λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}, I→R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$I\\rightarrow R$$\\end{document} after infection time τI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _I$$\\end{document} and R→I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R\\rightarrow I$$\\end{document} after recovery time τR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _R$$\\end{document}. In the case of τR>τI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _R>\ au _I$$\\end{document}, this model has been found to have two critical thresholds separating the active phase from absorbing phases. The first critical threshold λc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c1}$$\\end{document} corresponds to a low infection probability and the second critical threshold λc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c2}$$\\end{document} corresponds to a high infection probability. At the first critical threshold λc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c1}$$\\end{document}, our Monte Carlo simulations of this model suggest the phase transition to be of directed percolation class (DP). However, at the second critical threshold λc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c2}$$\\end{document} we observe that the system becomes so sensitive to initial values conditions which suggest the phase transition to be a discontinuous transition. We confirm this result using order parameter quasistationary probability distribution and finite-size analysis for this model at λc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _{c2}$$\\end{document}.

Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension D ≤ 2. For long-range interactions with a power-law form (1/rα), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when α ≥ 2D. However, the situation for α ∈ (2, 4) at D = 2 is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of SU(2) symmetry in the ferromagnetic Heisenberg model with 1/rα-form long-range interactions at D = 2. We determine critical exponents through finite-size analysis for α < 3 (above the upper critical dimension with Gaussian fixed point) and 3 ≤ α < 4 (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem’s scope.

Quantum Complementarity Approach to Device-Independent Security.

Complementarity is an essential feature of quantum mechanics. The preparation of an eigenstate of one observable implies complete randomness in its complementary observable. In quantum cryptography, complementarity allows us to formulate security analyses in terms of phase-error correction. However, the concept becomes much subtler in the device-independent regime that offers security without device characterization. Security proofs of device-independent quantum cryptography tasks are often complex and quite different from those of their more standard device-dependent cousins. The existing proofs pose huge challenges to experiments, among which large data-size requirement is a crux. Here, we show the complementarity security origin of the device-independent tasks. By linking complementarity with quantum nonlocality, we recast the device-independent scheme into a quantum error correction protocol. Going beyond the identical-and-independent-distribution case, we consider the most general attack. We generalize the sample entropy in classical Shannon theory for the finite-size analysis. Our method exhibits good finite-size performance and brings the device-independent scheme to a more practical regime. Applying it to the data in a recent ion-trap-based device-independent quantum key distribution experiment, one could reduce the requirement on data size to less than a third. Furthermore, the operational meaning of complementarity naturally extends device-independent scenarios to advantage key distillation, easing experiments by tolerating higher loss and lower transmittance.

Finite-size analysis in neural network classification of critical phenomena.

We analyze the problem of supervised learning of ferromagnetic phase transitions from the statistical physics perspective. We consider two systems in two universality classes, the two-dimensional Ising model and two-dimensional Baxter-Wu model, and perform careful finite-size analysis of the results of the supervised learning of the phases of each model. We find that the variance of the neural network (NN) output function (VOF) as a function of temperature has a peak in the critical region. Qualitatively, the VOF is related to the classification rate of the NN. We find that the width of the VOF peak displays the finite-size scaling governed by the correlation length exponent ν of the universality class of the model. We check this conclusion using several NN architectures-a fully connected NN, a convolutional NN, and several members of the ResNet family-and discuss the accuracy of the extracted critical exponents ν.

Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution

Recent studies showed the finite-size security of binary-modulation CV-QKD protocols against general attacks. However, they gave poor key-rate scaling against transmission distance. Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with the reverse reconciliation under the finite-size regime and obtain large improvements in the key rates. Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses. This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.

Uq[OSp(3|2)] quantum chains with quantum group invariant boundaries

Based on the finite-size analysis of the spectrum of the quantum group invariant deformation of the OSp(3|2) superspin chain we identify the operator content of the conformal field theory describing the model in its scaling limit. We find that the macroscopic degeneracy of the conformal weights observed in the thermodynamic limit of the isotropic superspin chain is lifted by the deformation.

Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy

ABSTRACT The three-dimensional anisotropic classical XY ferromagnet has been investigated by extensive Monte Carlo simulation using the Metropolis single spin flip algorithm. The magnetisation (M) and the susceptibility (χ) are measured and studied as functions of the temperature of the system. For constant anisotropy, the ferro-para phase transition has been found to take place at a higher temperature than that observed in the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The opposite scenario is observed in the case of random anisotropy. For all three different kinds of statistical distributions (uniform, Gaussian, and bimodal) of random anisotropy, the system gets ordered at lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the phase boundaries in the case of random anisotropy. The critical exponents for the scaling laws and are estimated through the finite size analysis.

Neural Network-Based Prediction for Secret Key Rate of Underwater Continuous-Variable Quantum Key Distribution through a Seawater Channel.

Continuous-variable quantum key distribution (CVQKD) plays an important role in quantum communications, because of its compatible setup for optical implementation with low cost. For this paper, we considered a neural network approach to predicting the secret key rate of CVQKD with discrete modulation (DM) through an underwater channel. A long-short-term-memory-(LSTM)-based neural network (NN) model was employed, in order to demonstrate performance improvement when taking into account the secret key rate. The numerical simulations showed that the lower bound of the secret key rate could be achieved for a finite-size analysis, where the LSTM-based neural network (NN) was much better than that of the backward-propagation-(BP)-based neural network (NN). This approach helped to realize the fast derivation of the secret key rate of CVQKD through an underwater channel, indicating that it can be used for improving performance in practical quantum communications.

Detecting quantum phase transitions in the quasistationary regime of Ising chains

Recently, single-site observables have been shown to be useful for probing critical slowing down in sudden quench dynamics [Da\ifmmode \breve{g}\else \u{g}\fi{} et al., Phys. Rev. B 107, L121113 (2023)]. Here, we demonstrate the potential of single-site magnetization as a probe of quantum phase transitions in integrable and nonintegrable transverse-field Ising chains (TFIC). We analytically prove the requirement of zero modes for the quasistationary regime to emerge at a probe site near the edge, and show how this regime gives rise to a nonanalytic behavior in the dynamical order profiles. Our $\mathit{t}$-DMRG calculations verify the results of the quench mean-field theory for near-integrable TFIC both with finite-size and finite-time scaling analyses. We find that both finite-size and finite-time analyses suggest a dynamical critical point for a strongly nonintegrable and locally connected TFIC. We finally demonstrate the presence of a quasistationary regime in the power-law interacting TFIC, and extract local dynamical order profiles for TFIC in the long-range Ising universality class with algebraic light cones.

Critical and topological phases of dimerized Kitaev chain in presence of quasiperiodic potential

We investigate localization and topological properties of a dimerized Kitaev chain with $p$-wave superconducting correlations and a quasiperiodically modulated chemical potential. With regard to the localization studies, we demonstrate the existence of distinct phases, such as, the extended phase, the critical (intermediate) phase, and the localized phase that arise due to the competition between the dimerization and the on-site quasiperiodic potential. Most interestingly, the critical phase comprises of two different anomalous mobility edges that are found to exist between the extended to the localized phase, and between the critical (multifractal) and localized phases. We perform our analysis employing the inverse and the normalized participation ratios, fractal dimension, and the level spacing. Subsequently, a finite-size analysis is done to provide support of our findings. Furthermore, we study the topological properties of the zero-energy edge modes via computing the real-space winding number and number of the Majorana zero modes present in the system. We specifically illustrate that our model exhibits a phase transition from a topologically trivial to a nontrivial phase (topological Anderson phase) beyond a critical dimerization strength under the influence of the quasiperiodic potential strength. Finally, in presence of a large potential, we demonstrate that the system undergoes yet another transition from the topologically nontrivial to an Anderson localized phase. Thus, we believe that our results will aid exploration of fundamentally different physics pertaining to the critical and the topological Anderson phases.

Improved DIQKD protocols with finite-size analysis

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on noisy preprocessing, random key measurements, and modified CHSH inequalities. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of 9.33&amp;#x0025;, exceeding all previously known noise thresholds. We also develop a modification to random-key-measurement protocols, using a pre-shared seed followed by a "seed recovery" step, which yields substantially higher net key generation rates by essentially removing the sifting factor. Some of our results may also improve the keyrates of device-independent randomness expansion.

Many-body localization and the area law in two dimensions

We study the high-energy phase diagram of a two-dimensional spin-$\frac{1}{2}$ Heisenberg model on a square lattice in the presence of either quenched or quasiperiodic disorder. The use of large-scale tensor network numerics allows us to compute the bipartite entanglement entropy for systems of up to $60 \times 7$ lattice sites. We provide evidence for the existence of a many-body localized regime for large disorder strength that features an area law in excited states and that violates the eigenstate thermalization hypothesis. From a finite-size analysis, we determine an estimate for the critical disorder strength where the transition to the ergodic regime occurs in the quenched case.

Manipulating the non-Hermitian skin effect via electric fields

In non-Hermitian systems, the phenomenon that the bulk-band eigenstates are accumulated at the boundaries of the systems under open boundary conditions is called non-Hermitian skin effect (NHSE), which is one of the most iconic and important features of a non-Hermitian system. In this work, we investigate the fate of NHSE in the presence of electric fields by analytically calculating the dynamical evolution of an initial bulk state and numerically computing the spectral winding number, the distributions of eigenstates, as well as the dynamical evolutions. We show abundant manipulation effects of dc and ac fields on the NHSE, and that the physical mechanism behind these effects is the interplay between the Stark localization, dynamic localization and the NHSE. In addition, the finite size analysis of the non-Hermitian system with a pure dc field shows the phenomenon of size-dependent NHSE. We further propose a scheme to realize the discussed model based on an electronic circuit. The results will help to deepen the understanding of NHSE and its manipulation.

Antiferromagnetism beyond the classical percolation threshold in the diluted half-filled one-band Hubbard model in three dimensions

We investigate the impact of site dilution by setting the on-site repulsion strength ($U$) to zero at a fraction of sites in the half-filled Hubbard model on a simple cubic lattice. We employ a semi-classical Monte-Carlo approach first to recover the zero dilution (undiluted $x=1$) properties, including $U$ dependence of insulator to metal crossover temperature scale $T^*$ and long-range staggered antiferromagnetic ordering temperature ($T_N$). For the non-perturbative regime of $U \sim$ bandwidth, we find a rapid suppression of $T^*$ with reducing $x$ from 1 to 0.7. However, $T_N$ remains unchanged in this dilution range, showing a weakening of the insulating state but not of the magnetic order. At $x \leq 0.7$, $T^*$ and $T_N$ coincide and are suppressed together with further increase in site-dilution. Finally, the system loses the magnetic order and the insulating state for $x=0.15$, significantly below the classical percolation threshold $x_p^{sc} (\sim 0.31$). We show that the induced moments on $U=0$ sites drive the magnetic order below the classical percolation limit by studying local moment systematics and finite-size analysis of magnetic order. At the end, we show that either increasing $U$ to large values or raising temperature beyond a $U$ dependent critical value, suppresses the induced local moments of the $U=0$ sites and recovers the classical percolation threshold.