Pattern Of Entanglement Research Articles

A Simple Novel Technique of Infrared Meibography by Means of Spectral-Domain Optical Coherence Tomography: A Cross-Sectional Clinical Study.

PurposeTo compare a novel spectral-domain optical coherence tomography (SD-OCT) technique with traditional lid transillumination for evaluation of meibomian glands (MGs) and to assess the relation of MG morphologic changes to the glandular atrophy.DesignEvaluation of diagnostic technology.ParticipantsSixty-one patients with obstructive MGD (30 men, 31 women; age [mean ± standard deviation] 45.1 ± 12.1 years), and 75 control subjects (32 men, 43 women; 44.1 ± 12.5 years) were recruited in order to have a balanced distribution of glandular features.MethodsAgreement between SD-OCT and lid transillumination examination for the detection of drop-out (partial or complete loss of MGs) and microscopic changes (i.e. shortening, distortion, segmentation and entanglement), as well as the relationship between morphological features and MG atrophy were evaluated.Main Outcome MeasuresAgreement between the two meibographic techniques, bias in symmetry of classification, and association analysis between microscopic changes and MG dropout.ResultsOverall agreement for all morphological features was substantial (Cohen kappa coefficient = 0.77; p<0.001), even if, the majority of disagreement occurred for cases with segmentation, where agreement was present in only 108 (81.82%) of 132 eyes with adequate images for interpretation, and where SD-OCT tended to diagnose more cases not detected by traditional lid transillumination (McNemar test, p<0.001). Moreover, segmentation and distortion pattern negatively correlated with the degree of drop-out, whereas shortening and entanglement pattern demonstrated only a weak correlation (Spearman’s ρ was -0.691, -0.491, -0.359, -0.385, respectively).ConclusionsEach method has its advantages but in general there was close agreement between these meibographic techniques, particularly for MG dropout, which supports the reliability of our novel, simple and patient-friendly SD-OCT approach.

Static and dynamical quantum correlations in phases of an alternating-fieldXYmodel

We investigate the static and dynamical patterns of entanglement in an anisotropic XY model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse XY model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a "factorization line" on the plane of system parameters, in which the zero temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a non-monotonic behavior of entanglement with respect to temperature in the anti-ferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information theoretic measures can be both ergodic as well as non-ergodic, depending on the system parameters.

Many-body localization and transition by density matrix renormalization group and exact diagonalization studies

A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high energy densities through a disorder driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target the entanglement patterns of highly excited states for MBL systems. By studying the one dimensional Heisenberg spin chain in a random field, we demonstrate the high accuracy of the method in obtaining statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks; one at zero and another one at the quantized entropy $S=ln2$ with an exponential decay tail on the $S>ln2$ side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop long-range power-law correlations. The corresponding phase diagram contains an intermediate regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in the intermediate regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.

Spread of entanglement and causality

We investigate causality constraints on the time evolution of entanglement entropy after a global quench in relativistic theories. We first provide a general proof that the so-called tsunami velocity is bounded by the speed of light. We then generalize the free particle streaming model of arXiv:cond-mat/0503393 to general dimensions and to an arbitrary entanglement pattern of the initial state. In more than two spacetime dimensions the spread of entanglement in these models is highly sensitive to the initial entanglement pattern, but we are able to prove an upper bound on the normalized rate of growth of entanglement entropy, and hence the tsunami velocity. The bound is smaller than what one gets for quenches in holographic theories, which highlights the importance of interactions in the spread of entanglement in many-body systems. We propose an interacting model which we believe provides an upper bound on the spread of entanglement for interacting relativistic theories. In two spacetime dimensions with multiple intervals, this model and its variations are able to reproduce intricate results exhibited by holographic theories for a significant part of the parameter space. For higher dimensions, the model bounds the tsunami velocity at the speed of light. Finally, we construct a geometric model for entanglement propagation based on a tensor network construction for global quenches.

Many-body localization and thermalization: Insights from the entanglement spectrum

We study the entanglement spectrum in the many body localizing and thermalizing phases of one and two dimensional Hamiltonian systems, and periodically driven `Floquet' systems. We focus on the level statistics of the entanglement spectrum as obtained through numerical diagonalization, finding structure beyond that revealed by more limited measures such as entanglement entropy. In the thermalizing phase the entanglement spectrum obeys level statistics governed by an appropriate random matrix ensemble. For Hamiltonian systems this can be viewed as evidence in favor of a strong version of the eigenstate thermalization hypothesis (ETH). Similar results are also obtained for Floquet systems, where they constitute a result `beyond ETH', and show that the corrections to ETH governing the Floquet entanglement spectrum have statistical properties governed by a random matrix ensemble. The particular random matrix ensemble governing the Floquet entanglement spectrum depends on the symmetries of the Floquet drive, and therefore can depend on the choice of origin of time. In the many body localized phase the entanglement spectrum is also found to show level repulsion, following a semi-Poisson distribution (in contrast to the energy spectrum, which follows a Poisson distribution). This semi-Poisson distribution is found to come mainly from states at high entanglement energies. The observed level repulsion only occurs for interacting localized phases. We also demonstrate that equivalent results can be obtained by calculating with a single typical eigenstate, or by averaging over a microcanonical energy window - a surprising result in the localized phase. This discovery of new structure in the pattern of entanglement of localized and thermalizing phases may open up new lines of attack on many body localization, thermalization, and the localization transition.

Superiority of photon subtraction to addition for entanglement in a multimode squeezed vacuum

We investigate the entanglement patterns of photon-added and -subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the "player" modes, the others being "spectators." We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast of the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state after photon subtraction can possess higher entanglement than that of the photon-added state, and we then compare it to that of the two-mode squeezed vacuum state. Moreover, we examine the non-Gaussianity of the photon-added and -subtracted states to find that the rich features provided by entanglement cannot be captured by the measure of non-classicality.

A theory of 2+1D bosonic topological orders

Abstract In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new ‘topological’ phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase—topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems).

Integral geometry and holography

We present a mathematical framework which underlies the connection be- tween information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts - points, distances and angles - are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entan- glement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.

Entanglement patterns and generalized correlation functions in quantum many-body systems

We introduce transition operators that in a given basis of the single-site states of a many-body system have a single nonvanishing matrix element and introduce their correlation functions. We show that they fall into groups that decay with the same rate. The mutual information defined in terms of the von Neumann entropy between two sites is given in terms of these so-called generalized correlation functions. We confirm numerically that the long-distance decay of the mutual information follows the square of that of the most slowly decaying generalized correlation function. The main advantage of our procedure is that, in order to identify the most relevant physical processes, there is no need to know a priori the nature of the ordering in the system, i.e., no need to explicitly construct particular physical correlation functions. We explore the behavior of the mutual information and the generalized correlation functions for comformally invariant models and for the $\text{SU}(n)$ Hubbard model with $n=2,3,4$, and 5, which are, in general, not conformally invariant. In this latter case, we show that for filling $f=1/q$ and $q&lt;n$, the ground state consists of highly entangled $q$-site units that are further entangled by single bonds. In addition, we extend the picture of the two-site mutual information and the corresponding generalized correlation functions to the $n$-site case.

Entanglement structures in qubit systems

Using measures of entanglement such as negativity and tangles we provide a detailed analysis of entanglement structures in pure states of non-interacting qubits. The motivation for this exercise primarily comes from holographic considerations, where entanglement is inextricably linked with the emergence of geometry. We use the qubit systems as toy models to probe the internal structure, and introduce some useful measures involving entanglement negativity to quantify general features of entanglement. In particular, our analysis focuses on various constraints on the pattern of entanglement which are known to be satisfied by holographic sates, such as the saturation of Araki–Lieb inequality (in certain circumstances), and the monogamy of mutual information. We argue that even systems as simple as few non-interacting qubits can be useful laboratories to explore how the emergence of the bulk geometry may be related to quantum information principles.

Constraints on the quantum state of pairs produced by semiclassical black holes

The pair-production process for a black hole (BH) is discussed within the framework of a recently proposed semiclassical model of BH evaporation. Our emphasis is on how the requirements of unitary evolution and strong subadditivity act to constrain the state of the produced pairs and their entanglement with the already emitted BH radiation. We find that the state of the produced pairs is indeed strongly constrained but that the semiclassical model is consistent with all requirements. We are led to the following picture: Initially, the pairs are produced in a state of nearly maximal entanglement amongst the partners, with a parametrically small entanglement between each positive-energy partner and the outgoing radiation, similar to Hawking’s model. But, as the BH evaporation progresses past the Page time, each positive-energy partner has a stronger entanglement with the outgoing radiation and, consequently, is less strongly entangled with its negative-energy partner. We present some evidence that this pattern of entanglement does not require non-local interactions, only EPR-like non-local correlations.

CpG signalling, H2A.Z/H3 acetylation and microRNA-mediated deferred self-attenuation orchestrate foetal NOS3 expression.

BackgroundAn adverse intrauterine environment leads to permanent physiological changes including vascular tone regulation, potentially influencing the risk for adult vascular diseases. We therefore aimed to monitor responsive NOS3 expression in human umbilical artery endothelial cells (HUAEC) and to study the underlying epigenetic signatures involved in its regulation.ResultsNOS3 and STAT3 mRNA levels were elevated in HUAEC of patients who suffered from placental insufficiency. 5-hydroxymethylcytosine, H3K9ac and Histone 2A (H2A).Zac at the NOS3 transcription start site directly correlated with NOS3 mRNA levels. Concomitantly, we observed entangled histone acetylation patterns and NOS3 response upon hypoxic conditions in vitro. Knock-down of either NOS3 or STAT3 by RNAi provided evidence for a functional NOS3/STAT3 relationship. Moreover, we recognized massive turnover of Stat3 at a discrete binding site in the NOS3 promoter. Interestingly, induced hyperacetylation resulted in short-termed increase of NOS3 mRNA followed by deferred decrease indicating that NOS3 expression could become self-attenuated by co-expressed intronic 27 nt-ncRNA. Reporter assay results and phylogenetic analyses enabled us to propose a novel model for STAT3-3′-UTR targeting by this 27-nt-ncRNA.ConclusionsAn adverse intrauterine environment leads to adaptive changes of NOS3 expression. Apparently, a rapid NOS3 self-limiting response upon ectopic triggers co-exists with longer termed expression changes in response to placental insufficiency involving differential epigenetic signatures. Their persistence might contribute to impaired vascular endothelial response and consequently increase the risk of cardiovascular disease later in life.Electronic supplementary materialThe online version of this article (doi:10.1186/s13148-014-0042-4) contains supplementary material, which is available to authorized users.

Anatomie de la symphyse pubienne

Pubic symphysis is an original joint, because its vertical fibro-cartilaginous disc, inserted between the two ‘endplates’ of pubic bones, is reminiscent of a vertebral disc. It must resist compression, tearing, and shearing stresses, and physiological vertical shift can reach 2 mm and rotation 1°. During pregnancy, relaxin induces the resorption of the edges of symphysis, leading to widening of the joint. Structural changes within the disc also increase its mobility. Rectus abdominalis, adductor longus and obliquus externus control those shifts, but the sites of insertions of those muscles around the symphysis are still disputed. The pattern of entanglement of collagen fibers within the disc has been poorly studied. The same hold true for the central cleft, which develops over time, as also observed in some vertebral discs. The biomechanics and motility of symphysis according to sex and anatomic variations should be further studied, as well as the inter-individual changes in joint innervations, to better explain the changing occurrences of pubalgia across the population, either in sports or pregnancy.

Holographic relaxation of finite size isolated quantum systems

We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the traveling shell is brought into correspondence with the evolution of the entanglement pattern in the dual field theory. The entanglement entropy is not only able to portrait the streaming of entangled excitations, but it is also a useful probe of interaction effects.

Signature candidate of quantum chaos far from the semiclassical regime

We numerically investigated the entanglement product in the simplest coupled kicked top model with the spin j = 1. Different from the dynamical pattern of entanglement in the semiclassical regime, two similar initial states may have discordant entanglement oscillations. A candidate of the quantum signature of this classical chaotic system was proposed. The potential antimonotonic relation between the rank correlation coefficient qualifying the concordant of two entanglement evolutions and the stationary entanglement was preliminarily revealed.

Patterns of genuine multipartite entanglement in frustrated quantum spin systems

We investigate the behavior of genuine multipartite entanglement of paradigmatic frustrated quantum spin systems. We consider six different spin models, whose frustration ranges from being very high to very low. We find that the highly frustrated quantum spin systems are near-maximally genuine multipartite entangled, while those with low frustration do not possess a similar definite behavior with regard to their genuine multipartite entanglement.

Geometric entanglement in topologically ordered states

Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically ordered systems such as the toric code, double semion, colour code and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks and a contribution quantifying the underlying pattern of long-range entanglement of the topologically ordered state. This topological contribution is also present in the case of single-spin blocks in most cases, and constitutes an alternative characterization of topological order for these quantum states based on a multipartite entanglement measure. In particular, we see that the topological term for the two-dimensional colour code is twice as much as the one for the toric code, in accordance with recent renormalization group arguments (Bombin et al 2012 New J. Phys. 14 073048). Motivated by these results, we also derive a general formalism to obtain upper- and lower-bounds to the geometric entanglement of states with a non-Abelian group symmetry, and which we explicitly use to analyse quantum double models. Furthermore, we also provide an analysis of the robustness of the topological contribution in terms of renormalization and perturbation theory arguments, as well as a numerical estimation for small systems. Some of the results in this paper rely on the ability to disentangle single sites from the quantum state, which is always possible for the systems that we consider. Additionally we relate our results to the behaviour of the relative entropy of entanglement in topologically ordered systems, and discuss a number of numerical approaches based on tensor networks that could be employed to extract this topological contribution for large systems beyond exactly solvable models.

Unravelling the quantum-entanglement effect of noble gas coordination on the spin ground state of CUO

The accurate description of the complexation of the CUO molecule by Ne and Ar noble gas matrices represents a challenging task for present-day quantum chemistry. Especially, the accurate prediction of the spin ground state of different CUO--noble-gas complexes remains elusive. In this work, the interaction of the CUO unit with the surrounding noble gas matrices is investigated in terms of complexation energies and dissected into its molecular orbital quantum entanglement patterns. Our analysis elucidates the anticipated singlet--triplet ground-state reversal of the CUO molecule diluted in different noble gas matrices and demonstrates that the strongest uranium-noble gas interaction is found for CUOAr4 in its triplet configuration.

Entanglement of four qubit systems: A geometric atlas with polynomial compass I (the finite world)

We investigate the geometry of the four qubit systems by means of algebraic geometry and invariant theory, which allows us to interpret certain entangled states as algebraic varieties. More precisely we describe the nullcone, i.e., the set of states annihilated by all invariant polynomials, and also the so-called third secant variety, which can be interpreted as the generalization of GHZ-states for more than three qubits. All our geometric descriptions go along with algorithms which allow us to identify any given state in the nullcone or in the third secant variety as a point of one of the 47 varieties described in the paper. These 47 varieties correspond to 47 non-equivalent entanglement patterns, which reduce to 15 different classes if we allow permutations of the qubits.

Symmetry-protected quantum state renormalization

Symmetry protected topological (SPT) phases with gapless edge excitations have been shown to exist in principle in strongly interacting bosonic/fermionic systems and it is highly desirable to find practical systems to realize such phases through numerical calculation. A central question to be addressed is how to determine the SPT order in the system given the numerical simulation result while no local order parameter can be measured to distinguish the phases from a trivial one. In the tensor network approach to simulate strongly interacting systems, the quantum state renormalization algorithm has been demonstrated to be effective in identifying the intrinsic topological orders. Here we show that a modified algorithm can identify SPT orders by extracting the fixed point entanglement pattern in the ground state wave function which is essential for the existence of SPT order. The key to this approach is to add symmetry protection to the quantum state renormalization process and we demonstrate the effectiveness of this algorithm with the example of AKLT states in both 1D and 2D.