Geometric Coherence Research Articles

The dynamics of quantum correlations and quantum coherence ina classical colored noise

The dynamics of one-way information deficit, geometric quantum discord and quantum coherence in mixed bipartite qubit state in the presence of classical colored noise with 1/fα spectrum are investigated. The source of the noise spectrum is a single fluctuator with undetermined switching rate. The analysis is made under the frame work of collective coupling between the components of the system and environment. Qualitatively the responses of all the three quantities are similar to the noise, however, quantum coherence stands robust than the other two quantities. Depending on choice of the different regimes of the characteristic parameters of the noise, the decay in all the three quantities can be monotonic, damped oscillating or exhibiting sudden death with revivals.

POVM-induced Coherence Measure in Terms of Fidelity

Coherence theory has been studied for many years. It plays an important role in quantum information and quantum computation. Recently, Bischof established POVM-based coherence measures and POVM-incoherent operations that coincide for the case of von Neumann measurements with their counterparts in standard coherence theory. Following this theoretical framework, we study whether the geometric coherence based on fidelity meet the constraint for quantifying coherence.

The Impact of Multi-functionality in Promoting the Aesthetic Values of Modern Islamic Architecture

Relationship between function and aesthetic has been occupied researchers, philosophers, artists and architects considerably to define meanings and to show significance degree of mutual influences. This analytical research investigates – How multi-functionality improve aesthetic values of architectural forms in contemporary Islamic architecture. We have defined procedurally the concept of multi-functionality as a potential forces of generative centers and aesthetic as geometrical coherence of architectural form. The absence of clear relations between multi-functionality and how it can be used to improve aesthetic values formed a basic research problem. The main target of this research is to determine how designers can enhancing aesthetic values of forms by using different functions. We suppose that multi-functionality improve the aesthetic values of the architectural form by strengthening geometrical coherence. We selected Five projects of contemporary Islamic centers and sample of 20 person’s. Semantic differential scale was used to analyze variables. The research found that multi-functionality has a great role in supporting the aesthetic values of architectural form by defining physical characters, Identifying and intensifying its visual and physical connections.

Quantifying coherence in terms of the pure-state coherence

Quantifying quantum coherence is a key task in the resource theory of coherence. Here we establish a good coherence monotone in terms of a state conversion process, which automatically endows the coherence monotone with an operational meaning. We show that any state can be produced from some input pure states via the corresponding incoherent channels. It is found that the coherence of a given state can be well characterized by the least coherence of the input pure states, so a coherence monotone is established by only effectively quantifying the input pure states. In particular, we show that our proposed coherence monotone is the supremum of all the coherence monotones that give the same coherence for any given pure state. We also prove that our coherence monotone is continuous. Considering the convexity, we prove that our proposed coherence measure is a subset of the coherence measure based on the convex roof construction. The similarities and differences between our coherence monotone and coherence cost are studied in detail. As applications, we give a concrete expression of our coherence measure by employing the geometric coherence of a pure state. We also give a thorough analysis of the states of the qubit and finally obtain a series of analytic coherence measures. The numerical examples are also given to show the difference between our coherence monotone and that based on the convex roof construction.

Characterizing quantum correlation with the correlated part of partial coherence

One of the fundamental features of the quantum world that distinguishes it from the classical counterpart is the existence of quantum correlations. In this paper, we study the quantum correlation from the viewpoint of partial coherence. Partial coherence in a bipartite system often contains local coherence of a subsystem. By removing the local coherence, we show that the remaining part of partial coherence can be regarded as quantum correlations. In this way, we introduce two quantum correlations: partial correlated coherence (PCC) and minimal partial correlated coherence (MPCC). Furthermore, we prove that PCC and MPCC induced by contractive pseudodistances are good candidates of quantum correlations. For contractive pseudodistances, we also show that the induced geometric partial correlated coherence (GPCC) and geometric minimal partial correlated coherence are actually the upper and lower bound of corresponding geometric quantum discord. Particularly, GPCCs based on a family of distances are proved to be bona fide measures of quantum correlations. By connecting to local quantum uncertainty, we provide an operational meaning for geometric quantum discord and GPCC induced by affinity of distance.

Cretaceous extensional systems of the Golfo San Jorge basin: Insights from the analysis of fault length and displacement data

Displacement profiles and maps were used in the subsurface of the Golfo San Jorge basin in the Manantiales Behr region to analyze factors affecting the geometric and kinematic evolution of an extensional system and its relationship with the migration and trapping of hydrocarbons. Two fault types were recognized: faults affecting both the basement and the sedimentary cover, and faults restricted to the sedimentary cover. The vertical growth of the faults within the sedimentary cover was constrained by vertical lithologic variations and by intersection with the free surface. Faults involving the basement are synsedimentary and show Dmax/L relationships and aspect ratios that allow their distinction from the shallower fault planes. The geometric coherence shown in the aggregated displacement profile and map suggests a synchronous kinematic evolution for the faults developed inside the sedimentary cover. Observed fault trace lengths and throw values distributions may indicate that those faults grew by the early linkage of isolated fault segments followed by the progressive building of displacement. Reactivation of pre-existent basement fabric had little influence on faulting across overlying sedimentary cover probably because the fine-grained beds of Pozo D-129 Formation acted as a structural decoupling level. The low degree of connection between the shallow and deep portions of the faults disregards the hypothesis of vertical migration from a local source pod. The mapping of fault segments with higher values of displacement and the recognition of transfer zones may help to locate and delineate footwall hydrocarbon traps. Comparison and integration with other studies show that Cretaceous fault systems in the eastern Golfo San Jorge basin have grown mainly by rapid length establishment and subsequent displacement accumulation. Also, most of the basement-involved structures do not connect significantly with overlying fault arrays.

Quantum groups under very strong axioms

We study the intermediate quantum groups $H_N\subset G\subset U_N^+$. The basic examples are $H_N,K_N,O_N,U_N,H_N^+,K_N^+,O_N^+,U_N^+$, which form a cube. Any other example $G$ sits inside the cube, and by using standard operations, namely intersection $\cap$ and generation $ $, can be projected on the faces and edges. We prove that under the strongest possible axioms, namely (1) easiness, (2) uniformity, and (3) geometric coherence of the various projection operations, the 8 basic solutions are the only ones.

Geometric coherence and quantum state discrimination

The operational meaning of coherence measure lies at the very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to the minimum error probability to discriminate a set of pure states with von Neumann measurement. On the other hand, we also show that a task to ambiguously discriminate a set of linearly independent pure states can be regarded as a problem of calculating geometric coherence. That is, we reveal an equivalence relation between ambiguous quantum state discrimination and geometric coherence. Based on this equivalence, moreover, we improve the upper bound for geometric coherence and give the explicit expression of geometric coherence for a class of states. Besides, we establish a complementarity relation of geometric coherence and path distinguishability, with which the relationship between l1-norm of coherence and geometric coherence is obtained. Finally, with geometric coherence, we study multiple copies of quantum state discrimination and give an example to show how to discriminate two pure states.

On the role of dealing with quantum coherence in amplitude amplification

Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. As measures of coherence, the geometric coherence and the relative entropy of coherence are considered. In terms of the relative entropy of coherence, complementarity relations with the success probability seem to be the most expository. The general relations presented are illustrated within several model scenarios of amplitude amplification processes.

A New Methodology for the Structural Analysis of 3D Digitized Cultural Heritage through FEA

Finite Elements Analysis (FEA) is widely used for modelling stress behaviour in any mechanical system. The processing workflow starts from CAD 3D models representing the ideal shape of the object to be simulated. Such models are typically made of mathematical elements defining its geometrical components. Those are pre-processed before the simulation for creating a volumetric mesh out of the CAD model. Recently the use of FEA has also been extended to the simulation of ancient structures and artefacts, revealing significant potentialities for the conservation of Cultural Heritage. Unlike modern mechanical systems, heritage objects are usually altered by the time passed since their original creation, and the representation with a schematic CAD model may introduce an excessive level of approximation leading to wrong simulation results. In the last two decades, 3D documentation of CH has been developed through reality-based approaches. However, the related mesh models of the exterior surfaces are not proper for direct use in FEA. Such high-resolution surface meshes has to be converted to volumetric meshes made of tetrahedral or hexahedral elementary volumes and a limited number of external and internal nodes. The focus of this paper is on a new method aiming at generating the best possible 3D solid representation of a real artefact from its accurate reality-based surface model by reducing its number of nodes of several orders of magnitude while maintaining a geometrical coherence in the order of the measurement uncertainty of the 3D capturing technique used. The approach proposed is based on wise use of retopology procedures and a transformation of this retopologized model to a mathematical one made by NURBS surfaces, suitable for being processed by a volumetric mesh generator typically embedded in any standard FEM package. The resulting volumetric mesh allows obtaining FEA of ancient structures, providing a far better accurate simulation than those attainable by a rough CAD redrawing of the heritage asset of interest.

Ordering states with various coherence measures

Quantum coherence is one of the most significant theories in quantum physics. Ordering states with various coherence measures is an intriguing task in quantification theory of coherence. In this paper, we study this problem by use of four important coherence measures -- the $l_1$ norm of coherence, the relative entropy of coherence, the geometric measure of coherence and the modified trace distance measure of coherence. We show that each pair of these measures give a different ordering of qudit states when $d\geq 3$. However, for single-qubit states, the $l_1$ norm of coherence and the geometric coherence provide the same ordering. We also show that the relative entropy of coherence and the geometric coherence give a different ordering for single-qubit states. Then we partially answer the open question proposed in [Quantum Inf. Process. 15, 4189 (2016)] whether all the coherence measures give a different ordering of states.

Coherence and entanglement measures based on Rényi relative entropies

We study systematically resource measures of coherence and entanglement based on Rényi relative entropies, which include the logarithmic robustness of coherence, geometric coherence, and conventional relative entropy of coherence together with their entanglement analogues. First, we show that each Rényi relative entropy of coherence is equal to the corresponding Rényi relative entropy of entanglement for any maximally correlated state. By virtue of this observation, we establish a simple operational connection between entanglement measures and coherence measures based on Rényi relative entropies. We then prove that all these coherence measures, including the logarithmic robustness of coherence, are additive. Accordingly, all these entanglement measures are additive for maximally correlated states. In addition, we derive analytical formulas for Rényi relative entropies of entanglement of maximally correlated states and bipartite pure states, which reproduce a number of classic results on the relative entropy of entanglement and logarithmic robustness of entanglement in a unified framework. Several nontrivial bounds for Rényi relative entropies of coherence (entanglement) are further derived, which improve over results known previously. Moreover, we determine all states whose relative entropy of coherence is equal to the logarithmic robustness of coherence. As an application, we provide an upper bound for the exact coherence distillation rate, which is saturated for pure states.

Uncertainty relations for quantum coherence with respect to mutually unbiased bases

The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was studied by deriving upper bounds on the sum of the corresponding measures. To obtain a two-sided estimate, lower bounds on the coherence quantifiers are also of interest. Such bounds are naturally referred to as uncertainty relations for quantum coherence. We obtain new uncertainty relations for coherence quantifiers averaged with respect to a set of mutually unbiased bases (MUBs). To quantify the degree of coherence, the relative entropy of coherence and the geometric coherence are used. Further, we also derive novel state-independent uncertainty relations for a set of MUBs in terms of the min-entropy.

Quantum coherence and quantum phase transition in the XY model with staggered Dzyaloshinsky-Moriya interaction

We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.

Morphable Word Clouds for Time-Varying Text Data Visualization.

A word cloud is a visual representation of a collection of text documents that uses various font sizes, colors, and spaces to arrange and depict significant words. The majority of previous studies on time-varying word clouds focuses on layout optimization and temporal trend visualization. However, they do not fully consider the spatial shapes and temporal motions of word clouds, which are important factors for attracting people's attention and are also important cues for human visual systems in capturing information from time-varying text data. This paper presents a novel method that uses rigid body dynamics to arrange multi-temporal word-tags in a specific shape sequence under various constraints. Each word-tag is regarded as a rigid body in dynamics. With the aid of geometric, aesthetic, and temporal coherence constraints, the proposed method can generate a temporally morphable word cloud that not only arranges word-tags in their corresponding shapes but also smoothly transforms the shapes of word clouds over time, thus yielding a pleasing time-varying visualization. Using the proposed frame-by-frame and morphable word clouds, people can observe the overall story of a time-varying text data from the shape transition, and people can also observe the details from the word clouds in frames. Experimental results on various data demonstrate the feasibility and flexibility of the proposed method in morphable word cloud generation. In addition, an application that uses the proposed word clouds in a simulated exhibition demonstrates the usefulness of the proposed method.

Matching Images With Multiple Descriptors: An Unsupervised Approach for Locally Adaptive Descriptor Selection

With the aim to improve the performance of feature matching, we present an unsupervised approach for adaptive description selection in the space of homographies. Inspired by the observation that the homographies of correct feature correspondences vary smoothly along the spatial domain, our approach stands on the unsupervised nature of feature matching, and can choose a good descriptor locally for matching each feature point, instead of using one global descriptor. To this end, the homography space serves as the domain for selecting various heterogeneous descriptors. Correspondences obtained by any descriptors are considered as points in the space, and their geometric coherence and spatial continuity are measured via computing the geodesic distances. In this way, mutual verification across different descriptors is allowed, and correct correspondences will be highlighted with a high degree of consistency short geodesic distances here. It follows that one-class SVM can be applied to identifying these correct correspondences, and achieves adaptive descriptor selection. The proposed approach is comprehensively compared with the state-of-the-art approaches, and evaluated on five benchmarks of image matching. The promising results manifest its effectiveness.

Second-Order Configuration of Local Features for Geometrically Stable Image Matching and Retrieval

Local features offer high repeatability, which supports efficient matching between images, but they do not provide sufficient discriminative power. Imposing a geometric coherence constraint on local features improves the discriminative power but makes the matching sensitive to anisotropic transformations. We propose a novel feature representation approach to solve the latter problem. Each image is abstracted by a set of tuples of local features. We revisit affine shape adaptation and extend its conclusion to characterize the geometrically stable feature of each tuple. The representation thus provides higher repeatability with anisotropic scaling and shearing than found in previous research. We develop a simple matching model by voting in the geometrically stable feature space, where votes arise from tuple correspondences. To make the required index space linear as regards the number of features, we propose a second approach called a centrality-sensitive pyramid to select potentially meaningful tuples of local features on the basis of their spatial neighborhood information. It achieves faster neighborhood association and has a greater robustness to errors in interest point detection and description. We comprehensively evaluated our approach using Flickr Logos 32, Holiday, Oxford Buildings, and Flickr 100 K benchmarks. Extensive experiments and comparisons with advanced approaches demonstrate the superiority of our approach in image retrieval tasks.

Efficient computation of cross-sections from human brain model by geometric processing

In this paper, an efficient method for computing the cross-sections of the internal structure from a 3D human brain model has been proposed. It can extract image slices from the brain model in sagittal, coronal, and axial views used for computed tomography and ultrasonography. A doubly connected edge list (DCEL) has been used for speeding up the computation during geometric processing, since the DCEL captures the topological relationship among vertices, edges, and faces of the triangulated surface. For a sectional plane, image slices are computed quite efficiently using the information of geometric coherence from the previous sectional plane with the help of DCEL. The optimal distance between two successive sectional planes is determined from the frequency distribution (Poisson distribution) of the edge lengths in the model. It reduces computational overhead without compromising on the quality of output, as demonstrated by experimental results.

The Geometry of Bourges Cathedral

This article presents a geometrical analysis of Bourges Cathedral, based on the application of computer-aided design (CAD) techniques to the results of a recent and highly precise laser survey. This analysis reveals that the cathedral's original designer developed a tightly interlocking and strikingly unified design, in which the five-fold subdivision of the chevet ground plan set proportions that would be vertically extruded into an elevation that can be inscribed both within a square and within a series of progessively smaller equilaterial triangles. These results contribute to an ongoing debate about the use of ‘ad quadratum’ and ‘ad triangulum’ geometries in Gothic architecture, and they provide new evidence for the geometrical coherence of Gothic cathedral design. In methodological terms, meanwhile, this discussion demonstrates the potential of CAD-based geometrical analysis for the study of precisely surveyed medieval buildings. The sequence of images being analysed can be viewed as supplementary material at: http://dx.doi.org/10.5334/ah.bz.s1

An Object-Based Hierarchical Method for Change Detection Using Unmanned Aerial Vehicle Images

There have been increasing demands for automatically monitoring urban areas in very high detail, and the Unmanned Aerial Vehicle (UAV) with auto-navigation (AUNA) system offers such capability. This study proposes an object-based hierarchical method to detect changes from UAV images taken at different times. It consists of several steps. In the first step, an octocopter with AUNA capability is used to acquire images at different dates. These images are registered automatically, based on SIFT (Scale-Invariant Feature Transform) feature points, via the general bundle adjustment framework. Thus, the Digital Surface Models (DSMs) and orthophotos can be generated for raster-based change analysis. In the next step, a multi-primitive segmentation method combining the spectral and geometric information is proposed for object-based analysis. In the final step, a multi-criteria decision analysis is carried out concerning the height, spectral and geometric coherence, and shape regularity for change determination. Experiments based on UAV images with five-centimeter ground resolution demonstrate the effectiveness of the proposed method, leading to the conclusion that this method is practically applicable for frequent monitoring.