arXiv subjects

Gábor Drótos

Publications and source records attributed to Gábor Drótos.

10 recordsLinked to original sources

arXiv2025

Certifying asymmetry in the configuration of three qubits

Symmetry restrictions limit the types of tasks that can be achieved with a given set of quantum states. Therefore, any breaking of these symmetries could potentially be exploited as a resource for quantum communication. Here we demonstrate this operationally by certifying asymmetry in the configuration of the Bloch vectors of a set of three unknown qubit states within the dimensionally bounded prepare-and-measure scenario. To do this, we construct a linear witness from three simpler witnesses as building blocks, each featuring, along with two binary measurement settings, three preparations; two of them are associated with the certification task, while the third one serves as an auxiliary. The final witness is chosen to self-test some target configuration. We numerically derive a bound $Q_{\text{mirror}}$ for any mirror-symmetric configuration, thereby certifying asymmetry if this bound is exceeded (e.g. experimentally) for the unknown qubit configuration. We also consider the gap $(Q_{\text{max}}-Q_{\text{mirror}})$ between the analytically derived overall quantum maximum $Q_{\text{max}}$ and the mirror-symmetric bound, and use it as a quantifier of asymmetry in the target configuration. Numerical optimization shows that the most asymmetric configuration then forms a right scalene triangle on the unit Bloch sphere. Finally, we implement our protocol on a public quantum processor, where a clear violation of the mirror-symmetric bound certifies asymmetry in the configuration of our experimental triple of qubit states.

quant-ph↗

arXiv2025

Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario

Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. In this study, we focus on the self-testing of a specific type of non-projective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome non-projective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete (semi-SIC) POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytical techniques for semi-DI self-testing in the PM scenario. Our results shall pave the way towards self-testing any extremal qubit POVM within a potentially minimal PM scenario.

quant-ph↗

arXiv2025

Classical bounds on two-outcome bipartite Bell expressions and linear prepare-and-measure witnesses: Efficient computation in parallel environments such as graphics processing units

The presented program aims at speeding up the brute force computation of the so-called $L_d$ norm of a matrix $M$ using graphics processing units (GPUs). Alternatives for CPUs have also been implemented, and the algorithm is applicable to any parallel environment. The $n\times m$ matrix $M$ has real elements which may represent coefficients of a bipartite Bell expression or those of a linear prepare-and-measure (PM) witness. In this interpretation, the $L_1$ norm is the local bound of the given correlation-type Bell expression, and the $L_d$ norm for $d\ge 2$ is the classical $d$-dimensional bound of the given PM witness, which is associated with the communication of $d$-level classical messages in the PM scenario. The program is also capable of calculating the local bound of Bell expressions including marginals. In all scenarios, the output is assumed to be binary. The code for GPUs is written in CUDA C and can utilize one NVIDIA GPU in a computer. To illustrate the performance of our implementation, we refer to Brierley et al. [arXiv:1609.05011] who needed approximately three weeks to compute the local bound on a Bell expression defined by a $42\times 42$ matrix on a standard desktop using a single CPU core. In contrast, our efficient implementation of the brute force algorithm allows us to reduce this to three minutes using a single NVIDIA RTX 6000 Ada graphics card on a workstation. For CPUs, the algorithm was implemented with OpenMP and MPI according to the shared and distributed memory models, respectively, and achieves a comparable speedup at a number of CPU cores around 100.

quant-ph↗

arXiv2024

Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios

Self-testing is a promising approach to certifying quantum states or measurements. Originally, it relied solely on the outcome statistics of the measurements involved in a device-independent (DI) setup. Extra physical assumptions about the system make the setup semi-DI. In the latter approach, we consider a prepare-and-measure scenario in which the dimension of the mediating particle is assumed to be two. In a setup involving four (three) preparations and three (two) projective measurements in addition to the target, we exemplify how to self-test any four- (three-) outcome extremal positive operator-valued measure using a linear witness. One of our constructions also achieves self-testing of any number of states with the help of as many projective measurements as the dimensionality of the space spanned by the corresponding Bloch vectors. These constructions are conjectured to be minimal in terms of the number of preparations and measurements required. In addition, we implement one of our prepare-and-measure constructions on IBM and IonQ quantum processors and certify the existence of a complex qubit Hilbert space based on the data obtained from these experiments.

quant-ph↗

arXiv2021

Network and geometric characterization of three-dimensional fluid transport between two layers

We consider transport in a fluid flow of arbitrary complexity but with a dominant flow direction. This is the situation encountered, for example, when analyzing the dynamics of sufficiently small particles immersed in a turbulent fluid and vertically sinking because of their weight. We develop a formalism characterizing the dynamics of particles released from one layer of fluid and arriving in a second one after traveling along the dominant direction. The main ingredient in our study is the definition of a two-layer map that describes the Lagrangian transport between both layers. We combine geometric approaches and probabilistic network descriptions to analyze the two-layer map. From the geometric point of view, we express the properties of lines, surfaces and densities transported by the flow in terms of singular values related to Lyapunov exponents, and define a new quantifier, the Finite Depth Lyapunov Exponent. Within the network approach, degrees and an entropy are introduced to characterize transport. We also provide relationships between both methodologies. The formalism is illustrated with numerical results for a modification of the ABC flow, a model commonly studied to characterize three-dimensional chaotic advection.

physics.flu-dyn↗

arXiv2021

Local characterization of transient chaos on finite times in open systems

To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate that these quantifiers have a considerable spread across the domain of the dynamics, but their spatial variation, especially on long but non-asymptotic integration times, is approximately consistent with the relationship that was recognized by Kantz and Grassberger for temporally asymptotic quantifiers. In particular, deviations from this relationship are smaller than differences between various locations, which confirms the existence of such a dynamical law and the suitability of our quantifiers to represent underlying dynamical properties in the non-asymptotic regime.

cond-mat.stat-mech↗

arXiv2021

Sinking microplastics in the water column: simulations in the Mediterranean Sea

We study the vertical dispersion and distribution of negatively buoyant rigid microplastics within a realistic circulation model of the Mediterranean sea. We first propose an equation describing their idealized dynamics. In that framework, we evaluate the importance of some relevant physical effects: inertia, Coriolis force, small-scale turbulence and variable seawater density, and bound the relative error of simplifying the dynamics to a constant sinking velocity added to a large-scale velocity field. We then calculate the amount and vertical distribution of microplastic particles on the water column of the open ocean if their release from the sea surface is continuous at rates compatible with observations in the Mediterranean. The vertical distribution is found to be almost uniform with depth for the majority of our parameter range. Transient distributions from flash releases reveal a non-Gaussian character of the dispersion and various diffusion laws, both normal and anomalous. The origin of these behaviors is explored in terms of horizontal and vertical flow organization.

physics.flu-dyn↗

arXiv2020

Nonlinear forced change and nonergodicity: The case of ENSO-Indian monsoon and global precipitation teleconnections

We study the forced response of the teleconnection between the El Nino-Southern Oscillation (ENSO) and global precipitation in general and the Indian summer monsoon (IM) in particular in the Max Planck Institute Grand Ensemble. The forced response of the teleconnection is defined as the time-dependence of a correlation coefficient evaluated over the ensemble. The ensemble-wise variability is taken either wrt. spatial averages or dominant spatial modes in the sense of Maximal Covariance Analysis or Canonical Correlation Analysis or EOF analysis. We find that the strengthening of the ENSO-IM teleconnection is robustly or consistently featured in view of all four teleconnection representations, whether sea surface temperature (SST) or sea level pressure (SLP) is used to characterise ENSO, and both in the historical period and under the RCP8.5 forcing scenario. The main contributor to this strengthening in terms of a linear regression model is the regression coefficient, which can outcompete even a declining ENSO variability in view of using the SLP. We also find that the forced change of the teleconnection is typically nonlinear by (1) formally rejecting the hypothesis that ergodicity holds, i.e., that expected values of temporal correlation coefficients with respect to the ensemble equal the ensemble-wise correlation coefficient itself, and also showing that (2) the trivial contributions of the forced changes of e.g. the mean SST and/or precipitation to temporal correlations are insignificant here. We also provide, in terms of the test statistics, global maps of the degree of nonlinearity/nonergodicity of the forced change of the teleconnection between local precipitation and ENSO.

physics.ao-ph↗

arXiv2018

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows

In an incompressible flow, fluid density remains invariant along fluid element trajectories. This implies that the spatial distribution of non-interacting noninertial particles in such flows cannot develop density inhomogeneities beyond those that are already introduced in the initial condition. However, in certain practical situations, density is measured or accumulated on (hyper-) surfaces of dimensionality lower than the full dimensionality of the flow in which the particles move. An example is the observation of particle distributions sedimented on the floor of the ocean. In such cases, even if the initial distribution of noninertial particles is uniform within a finite support in an incompressible flow, advection in the flow will give rise to inhomogeneities in the observed density. In this paper we analytically derive, in the framework of an initially homogeneous particle sheet sedimenting towards a bottom surface, the relationship between the geometry of the flow and the emerging distribution. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet, and the projection of the deformed sheet onto the target surface. We point out that an extreme form of inhomogeneity, caustics, can develop for sheets. We exemplify our geometrical results with simulations of particle advection in a simple kinematic flow, study the dependence on various parameters involved, and illustrate that the basic mechanisms work similarly if the initial (homogeneous) distribution occupies a more general region of finite extension rather than a sheet.

physics.flu-dyn↗

arXiv2018

Reconsidering the relationship of the El Niño--Southern Oscillation and the Indian monsoon using ensembles in Earth system models

We study the relationship between the El Niño--Southern Oscillation (ENSO) and the Indian summer monsoon in ensemble simulations from state-of-the-art climate models, the Max Planck Institute Earth System Model (MPI-ESM) and the Community Earth System Model (CESM). We consider two simple variables: the Tahiti--Darwin sea-level pressure difference and the Northern Indian precipitation. We utilize ensembles converged to the system's snapshot attractor for analyzing possible changes (i) in the teleconnection between the fluctuations of the two variables, and (ii) in their climatic means. (i) With very high confidence, we detect an increase in the strength of the teleconnection, as a response to the forcing, in the MPI-ESM under historical forcing between 1890 and 2005, concentrated to the end of this period. We explain that our finding does not contradict instrumental observations, since their existing analyses regarding the nonstationarity of the teleconnection are either methodologically unreliable, or consider an ill-defined teleconnection concept. In the MPI-ESM we cannot reject stationarity between 2006 and 2099 under the Representative Concentration Pathway 8.5 (RCP8.5), and in a 110-year-long 1-percent pure CO2 scenario; neither can we in the CESM between 1960 and 2100 with historical forcing and RCP8.5. (ii) In the latter ensembles, the climatic mean is strongly displaced in the phase space projection spanned by the two variables. This displacement is nevertheless linear. However, the slope exhibits a strong seasonality, falsifying a hypothesis of a universal, emergent relationship between these two climatic means, excluding applicability in an emergent constraint.

physics.ao-ph↗