Local information as a resource in distributed quantum systems

A new paradigm for distributed quantum systems where information is a valuable resource is developed. After finding a unique measure for information, we construct a scheme for its manipulation in analogy with entanglement theory. In this scheme, instead of maximally entangled states, two parties distill local states. We show that, surprisingly, the main tools of entanglement theory are general enough to work in this opposite scheme. Up to plausible assumptions, we show that the amount of information that must be lost during the protocol of concentration of local information can be expressed as the relative entropy distance from some special set of states.     

Negative ratings play a positive role in information filtering

The explosive growth of information asks for advanced information filtering techniques to solve the so-called information overload problem. A promising way is the recommender system which analyzes the historical records of users’ activities and accordingly provides personalized recommendations. Most recommender systems can be represented by user-object bipartite networks where users can evaluate and vote for objects, and ratings such as “dislike” and “I hate it” are treated straightforwardly as negative factors or are completely ignored in traditional approaches. Applying a local diffusion algorithm on three benchmark data sets, MovieLens, Netflix and Amazon, our study arrives at a very surprising result, namely the negative ratings may play a positive role especially for very sparse data sets. In-depth analysis at the microscopic level indicates that the negative ratings from less active users to less popular objects could probably have positive impacts on the recommendations, while the ones connecting active users and popular objects mostly should be treated negatively. We finally outline the significant relevance of our results to the two long-term challenges in information filtering: the sparsity problem and the cold-start problem.     

Undetermined states: how to find them and their applications

We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are proposed. One is to establish the relation between codewords of the stabilizer quantum error correction codes (SQECCs) and the undetermined states. The other is to study the local complementation rules of the graph states. As an application, the undetermined states can be exploited in the quantum secret sharing scheme. The security is guaranteed by their undetermineness.     

Decorrelation Estimates for the Eigenlevels of the Discrete Anderson Model in the Localized Regime

The purpose of the present work is to establish decorrelation estimates for the eigenvalues of the discrete Anderson model localized near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other. As a consequence of these decorrelation estimates, we obtain the independence of the limits of the local level statistics at two distinct energies.     

Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn’s Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d ₁,..., d _n ) and (c ₁,..., c _n ) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form.     

A Transformer-Based Capsule Network for 3D Part–Whole Relationship Learning

Learning the relationship between the part and whole of an object, such as humans recognizing objects, is a challenging task. In this paper, we specifically design a novel neural network to explore the local-to-global cognition of 3D models and the aggregation of structural contextual features in 3D space, inspired by the recent success of Transformer in natural language processing (NLP) and impressive strides in image analysis tasks such as image classification and object detection. We build a 3D shape Transformer based on local shape representation, which provides relation learning between local patches on 3D mesh models. Similar to token (word) states in NLP, we propose local shape tokens to encode local geometric information. On this basis, we design a shape-Transformer-based capsule routing algorithm. By applying an iterative capsule routing algorithm, local shape information can be further aggregated into high-level capsules containing deeper contextual information so as to realize the cognition from the local to the whole. We performed classification tasks on the deformable 3D object data sets SHREC10 and SHREC15 and the large data set ModelNet40, and obtained profound results, which shows that our model has excellent performance in complex 3D model recognition and big data feature learning.     

Controlled Remote State Preparation of an Arbitrary Two-Qubit State by Using Two Sets of Four-Qubit GHZ States

Recently, Huang and Zhao (Int. J. Theor. Phys. 56, 678, 2017) proposed a new scheme for controlled remote state preparation of an arbitrary two-qubit state by using two sets of three-qubit GHZ states as the quantum channel. In the scheme, Alice and Bob choose four different kinds of two-qubit projective measurement bases to measure their local qubits, respectively. We demonstrate that two sets of four-qubit GHZ states can be used to realize the deterministic controlled remote state preparation of an arbitrary two-qubit state by performing only two-qubit projective measurements.     

Local Copying of <Emphasis Type="Italic">d</Emphasis>×<Emphasis Type="Italic">d</Emphasis>-dimensional Partially Entangled Pure States

We examine the problem of copying a set of orthogonal, entangled partially (non-maximally) bipartite pure states with an entangled blank state under the restriction to local operations and classical communication (LOCC), and show a protocol for copying these states by LOCC. The necessary and sufficient condition for locally copying partially entangled pure states is then represented. As a result, we find that the problem of local copying these entangled states can be regarded to some extent as that of catalytic transformation between them by LOCC.     

Lower bound of local quantum uncertainty for high-dimensional bipartite quantum systems

Quantum correlations are of fundamental importance in quantum phenomena and studies related to quantum information processing. The measurement of quantum correlations is a central challenge. A recently proposed measure of quantum correlations,local quantum uncertainty(LQU), satisfies all the physical requirements as a measure of quantum correlations. This study derives a closed-form lower bound of the LQU for arbitrary-dimensional bipartite quantum states using operator relaxation. We also compared the lower bound with the optimized LQU for several typical sets of quantum states. The results show that the lower bound is near to the optimized LQU for three-dimensional bipartite quantum systems.     

Dynamics of impurity: Local and non-local information for two non-identical qubits

From the separability point of view the problem of two ions interact with a single cavity mode is investigated. The density matrix is calculated and used to discuss the entanglement and to examine the dynamics of the local and non-local information. Our examination concentrated on the variation in the mean photon number and the ratio of the coupling parameters. Furthermore, we have also assumed that the atomic system is initially in the ground states as well as in the intermediate states. It has been shown that the local information is transferred to non-local information when the impurity of one qubit or both is maximum.     

Flow estimation using an intravascular imaging catheter

Coronary flow assessment can be useful for determining the hemodynamic severity of a stenosis and to evaluate the outcome of interventional therapy. We developed a method for measuring the transverse flow through the imaging plane of an intravascular ultrasound (IVUS) catheter. This possibility has raised great clinical interest since it permits simultaneous assessment of vessel geometry and function with the same device. Furthermore, it should give more accurate information than combination devices because lumen diameter and velocity are determined at the same location. Flow velocity is estimated based on decorrelation estimation from sequences of radiofrequency (RF) traces acquired at nearly the same position. Signal gating yields a local estimate of the velocity. Integrating the local velocity over the lumen gives the quantitative flow. This principle has been calibrated and tested through computer modeling, in vitro experiments using a flow phantom and in vivo experiments in a porcine animal model, and validated against a Doppler element containing guide wire (Flowire) in humans. Originally the method was developed and tested for a rotating single element device. Currently the method is being developed for an array system. The great advantage of an array over the single element approach would be that the transducer has no intrinsic motion. This intrinsic motion sets a minimal threshold in the detectable velocity components. Although the principle is the same, the method needs some adaptation through the inherent different beamforming of the transducer. In this paper various aspects of the development of IVUS flow are reviewed.     

Laser speckle decorrelation in NDT

The random noise of the laser speckle field which develops at the focusing plane of an imaging system, is, by now, efficiently used in several interferometric techniques as an information carrier of the macroscopic wavefront distortion induced by the surface displacement field of the object under investigation. The actual noise in this kind of techniques is represented by the speckle decorrelation at the image plane — i.e. the destruction of the carrier — which may be caused by the modification of the texture surface (e.g. by yielding under a severe stress state), but it is inherently produced by the same displacement field under measurement. In the paper the phenomenon of laser speckle decorrelation is numerically simulated and experimentally investigated with the aim of estimating its sensitivity to local deformation and assessing a possible field of application. Satisfactory results in the field of NDT of multilayer fiber-reinforced composites were obtained by reducing the diaphragm of the lens to increase the sensitivity of the imaging system to speckle decorrelation induced by local deformation; unfortunately this simple approach requires a considerable amount of laser power for illuminating the object. Different aperture shapes were therefore numerically simulated which provided improved efficiency and sensitivity and whereby a semi-quantitative analysis of the displacement field could be experimented.     

Additive-subtractive phase-modulated speckle interferometry: Fringe visibility under partial decorrelation

Additive-subtractive phase modulated speckle interferometry (ASPMSI) is a technique that minimizes the susceptibility of speckle methods to environmental noise while providing fringes of good visibility. The method requires the acquisition of two consecutive video frames of additive-speckle images of the same two deformed states of an object at a rapid enough rate such that ambient noise is not a problem. The additive-speckle images as expected are of very poor visibility due to the presence of the self-interference term. An interframe phase-modulation is introduced and the two additive-speckle images are digitally subtracted to improve the fringe visibility by removing the self-interference term. The ASPM-SI method works with in-plane and out-of-plane deformation sensitive ESPI as well as with displacement-gradient sensitive speckle-shearing interferometry. It is shown that the ASPM-SI scheme has higher visibility than conventional additive-SI and performs consistently better than subtractive-SI schemes in the presence of partial interframe speckle decorrelating optical noise. Furthermore, it is shown that the fringe visibility of the out-of-plane displacement sensitive interferometer which uses a protected reference beam separate from the object beam can be made to be essentially unity even at complete interframe decorrelation.     

Masking Quantum Information Encoded in Pure and Mixed States

Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker S^? and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi’s paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry S^◇ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries S^? and S^◇, respectively.

     

Twist-teleportation-based local discrimination of maximally entangled states

In this work, we study the local distinguishability of maximally entangled states(MESs). In particular, we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensions. Fan and Tian et al. have already obtained two satisfactory results for the generalized Bell states(GBSs) and the qudit lattice states when applied to prime or prime power dimensions. We construct a general twist-teleportation scheme for any orthonormal basis with MESs that is inspired by the method used in [Phys. Rev. A 70, 022304(2004)]. Using this teleportation scheme, we obtain a sufficient and necessary condition for one-way distinguishable sets of MESs, which include the GBSs and the qudit lattice states as special cases.Moreover, we present a generalized version of the results in [Phys. Rev. A 92, 042320(2015)] for the arbitrary dimensional case.     

Self-Similarity of Edge Plasma Fluctuations in TEXTOR

In TEXTOR the long-range time dependence of edge plasma fluctuations has been investigated. The results indicate that the tail of the autocorrelation function decays as a power law for time lags longer than the local decorrelation time. The frequency spectra of the fluctuations show similar features to those obtained in "sandpile" models. Using rescaled range (R/S) analysis techniques the self-similarity parameters have been estimated for the potential fluctuation data detected by Langmuir probes. The results show that the Hurst exponents are well above 0.5 over the self-similarity range at all the measured radial locations. All these facts reveal the self-similar character of the electrostatic fluctuations at the plasma edge of TEXTOR, consistent with plasma transport as characterized by self-organized criticality (SOC). Furthermore, we have analyzed in this respect discharges in which an edge transport barrier was created by means of edge biasing, hitherto limited to floating potential measurements in the scrape off layer outside the barrier region. The results show a decrease of fluctuating amplitudes, a reduction of decorrelation time of local turbulence and, surprisingly, a concomitant increase of the Hurst exponent. This result implies that the mechanisms governing the decorrelation of local turbulence may differ from those governing the decorrelation of SOC transport events.     

Distinguishability of Quantum States Under Restricted Families of Measurements with an Application to Quantum Data Hiding

We consider the problem of ambiguous discrimination of two quantum states when we are only allowed to perform a restricted set of measurements. Let the bias of a POVM be defined as the total variational distance between the outcome distributions for the two states to be distinguished. The performance of a set of measurements can then be defined as the ratio of the bias of this POVM and the largest bias achievable by any measurements. We first provide lower bounds on the performance of various POVMs acting on a single system such as the isotropic POVM, and spherical 2 and 4-designs, and show how these bounds can lead to certainty relations. Furthermore, we prove lower bounds for several interesting POVMs acting on multipartite systems, such as the set of local POVMS, POVMs which can be implemented using local operations and classical communication (LOCC), separable POVMs, and finally POVMs for which every bipartition results in a measurement having positive partial transpose (PPT). In particular, our results show that a scheme of Terhal et. al. for hiding data against local operations and classical communication [31] has the best possible dimensional dependence.     

Infinite number of local conservation laws for the self-dual SU(2) Yang-Mills system within 't Hooft's ansatz

We derive infinite sets of local continuity equations for the four-dimensional classical self-dual SU(2) Yang-Mills fields subjected to 't Hooft's ansatz. In striking analogy to the two-dimensional CP(n) non-linear sigma model where local conservation laws obtain either from complex Cauchy-Riemann analyticity or from a matrix Riccati equation, our local sets derive from quaternionic Fueter analyticity or a Riccati equation associated with the geometric prolongation structure implied by the Belavin-Zakharov linear spectral problem for the self-dual Yang-Mills system. Our analysis underlines the close connection between local and non-local conservation laws and suggests that infinite sets of local continuity equations should be present in the general self-(antiself-)dual gauge field case.     

Anisotropy of spatiotemporal decorrelation in electrohydrodynamic turbulence

Nonlinear straining and random sweeping spatiotemporal decorrelation properties, originally introduced as the main processes for turbulent fluctuations decorrelation in usual fluid flows, have been observed experimentally in anisotropic electroconvective turbulence generated in a nematic liquid crystal under the action of an external oscillating electric field. A transition between both processes occurs when the instability is driven toward states of increasing complexity, thus showing that decorrelation mechanisms in turbulent media are more universal than naively expected. A model for both decorrelation mechanisms is introduced, its comparison with experimental results providing an estimate of the characteristic sweeping velocity.