Pattern Of Entanglement Research Articles

Contentious public finance: how entanglement shapes the costs of resisting elitist budgetary preferences

Entangled political economy views societal phenomena as featuring substantial interaction between economic and political entities, but questions have been raised about the conceptual properties of entanglement. The political economist Randall Holcombe has raised questions concerning the economic influences affecting uneven patterns of entanglement between entities. Drawing upon his own transaction costs-based framework of political stratification, Holcombe suggests that political elites incur relatively low transaction costs associated with bargaining over policies, whereas non-elites incur relatively high costs. This suggests that elites actively participate in policy design and implementation and can outmaneuver the non-elite public to externalize the costs of political decisions, yielding noticeable clustering effects within entangled network structures. This article seeks to build upon Holcombe’s insights, as well as the transaction cost politics of Charlotte Twight, illustrating how groups engaging in political processes attempt to manipulate transaction costs to secure favorable outcomes. Transaction cost manipulation by elites to secure advantages is commonly studied, but less so is how non-elitists succeed in adjusting the transaction costs of political exchanges to help prevent fiscal exploitation by elitists. The public finance case of Colorado’s Taxpayer’s Bill of Rights is used to illustrate how dynamic entanglements between elites and non-elites delivered institutional change better aligning with non-elite fiscal preferences.

Entanglement islands read perfect-tensor entanglement

In this paper, we make use of holographic Boundary Conformal Field Theory (BCFT) to simulate the black hole information problem in the semi-classical picture. We investigate the correlation between a portion of Hawking radiation and entanglement islands by the area of an entanglement wedge cross-section. Building on the understanding of the relationship between entanglement wedge cross-sections and perfect tensor entanglement as discussed in reference [18], we make an intriguing observation: in the semi-classical picture, the positioning of an entanglement island automatically yields a pattern of perfect tensor entanglement. Furthermore, the contribution of this perfect tensor entanglement, combined with the bipartite entanglement contribution, precisely determines the area of the entanglement wedge cross-section.

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are arranged in a spatially symmetric pattern and the states have maximal entanglement for all bipartitions that follow from the reflection symmetries of the given geometry. We consider those cases where the state itself is invariant with respect to the geometrical symmetry group. The simplest examples are those dual unitary operators which are also self dual and reflection invariant, but we also consider the generalizations in the hexagonal, cubic, and octahedral geometries. We provide a number of constructions and concrete examples for these objects for various local dimensions. All of our examples can be used to build quantum cellular automata in 1+1 or 2+1 dimensions, with multiple equivalent choices for the “direction of time”.

Mixformer: Mixture transformer with hierarchical context for spatio-temporal wind speed forecasting

Wind energy has attracted more and more attention due to its sustainability and pollution-free nature. As wind energy is highly dependent on wind speed, wind speed forecasting is of great importance for fully harvesting wind energy and ensuring the stability and reliability of wind energy systems. By accurately predicting the future wind speed, we can make efficient power schedules and consequently improve the utilization of wind power. Although existing forecasting methods have achieved satisfactory wind forecasting performance, they may still fail to discover the intricate spatio-temporal dependencies obscured in entangled patterns. To resolve this issue and further improve the prediction accuracy, we propose Mixformer, a novel mixture Transformer with hierarchical context for spatio-temporal wind speed forecasting. Mixformer first applies seasonal-trend decomposition, and then employs an MLP to predict the trend part and an attention model to predict the seasonal part. Besides, Mixformer innovatively proposes a spatio-temporal Gaussian mixture attention (ST-GMA) layer, which fuses the periodic temporal and long-term spatial context. To capture intricate long-term spatial characteristics, Mixformer extracts global information by the Dynamic Time Warping algorithm. Moreover, with the ST-GMA layer, Mixformer builds a hierarchical encoder–decoder architecture to fully utilize the context at different scales for seasonal forecasting and further enhance the spatio-temporal modeling. Empirical experiments on four real-world benchmark datasets show that Mixformer yields the lowest prediction errors with the MAE scores of 1.66, 1.68, 3.14 and 0.70 and the RMSE scores of 2.07, 2.01, 3.99 and 0.98, and improves the prediction accuracy by 8.43%, 5.36%, 4.14%, 6.57% in term of MAE scores and 9.18%, 6.92%, 4.01%, 5.75% in term of RMSE scores compared to state-of-the-art methods, which demonstrates the superiority of Mixformer. In a nutshell, Mixformer presents a promising method for spatio-temporal wind speed forecasting and may achieve desirable performance in real-world applications of wind power systems.

Short-term wind speed forecasting based on adaptive secondary decomposition and robust temporal convolutional network

Accurate and reliable short-term wind speed forecasting remains challenging due to the high volatility and randomness of wind speed. The secondary decomposition (SD) method deeply extracts the entangled fluctuation patterns by leveraging the advantages of two distinct decomposition methods. Nevertheless, two critical issues remain to be further explored, including (1) how to adaptively select the sub-signals to be further decomposed and (2) how to effectively capture the coupling temporal dependencies among the sub-signals. To address these issues, we propose a novel hybrid model based on an adaptive secondary decomposition (ASD) method and a robust temporal convolutional network (RTCN). Firstly, the proposed ASD method is developed to adaptively extract more sub-signals with lower complexities by combining the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), entropy-based spectral clustering (ESC), and the variational mode decomposition (VMD). Subsequently, a single RTCN is fitted to capture the temporal dependencies among the sub-signals and identify the global relationship between the sub-signals and the future wind speed. The forecasting performance is verified on four real-world wind speed datasets from different wind farms, and the experimental results demonstrate that the proposed ASD-RTCN model consistently outperforms the benchmark models in terms of forecasting accuracy and stability.

Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model

Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.

Physical entanglement between localized orbitals

The goal of the present work is to guide the development of quantum technologies in the context of fermionic systems. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This demonstrates the significance of the number-parity superselection rule and highlights the relevance of localized few-orbital subsystems for quantum information processing tasks. Then, we explore and quantify the entanglement between localized orbitals in two systems, a tight-binding model of non-interacting electrons and the hydrogen ring. For this, we apply the first closed formula of a faithful entanglement measure, derived in (arXiv:2207.03377) as an extension of the von Neumann entropy to genuinely correlated many-orbital systems. For both systems, long-distance entanglement is found at low and high densities η, whereas for medium densities, , practically only neighboring orbitals are entangled. The Coulomb interaction does not change the entanglement pattern qualitatively except for low and high densities where the entanglement increases as function of the distance between both orbitals.

Entanglement classification from a topological perspective

Classification of entanglement is an important problem in quantum resource theory. In this paper we discuss an embedding of this problem in the context of topological quantum field theories (TQFTs). This approach allows classifying entanglement patterns in terms of topological equivalence classes. In the bipartite case a classification equivalent to the one by stochastic local operations and classical communication (SLOCC) is constructed by restricting to a simple class of connectivity diagrams. Such diagrams characterize quantum states of TQFT up to braiding and tangling of the ``connectome.'' In the multipartite case the same restricted topological classification only captures a part of the SLOCC classes, in particular, it does not see the $W$ entanglement of three qubits. Nonlocal braiding of connections may solve the problem, but no finite classification is attempted in this case. Despite incompleteness, the connectome classification has a straightforward generalization to any number and dimension of parties and has a very intuitive interpretation, which might be useful for understanding specific properties of entanglement and for design of new quantum resources.

Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions

Entanglement comes in different forms, some more complex than others. In this paper we study the transitions of entanglement complexity in an exemplary family of states---the Rokhsar-Kivelson-sign wavefunctions---whose degree of entanglement is controlled by a single parameter. This family of states is known to feature a transition between a phase exhibiting volume-law scaling of entanglement entropy and a phase with subextensive scaling of entanglement, reminiscent of the many-body-localization transition of disordered quantum Hamiltonians. We study the singularities of the Rokhsar-Kivelson-sign wavefunctions and their entanglement complexity across the transition using several tools from quantum information theory: fidelity metric, entanglement spectrum statistics, entanglement entropy fluctuations, stabilizer R\'enyi entropy, and the performance of a disentangling algorithm. Across the whole volume-law phase the states feature universal entanglement spectrum statistics. Yet a ``superuniversal'' regime appears for small values of the control parameter in which all metrics become independent of the parameter itself, the entanglement entropy as well as the stabilizer R\'enyi entropy appear to approach their theoretical maximum, the entanglement fluctuations scale to zero as in output states of random universal circuits, and the disentangling algorithm has essentially null efficiency. All these indicators consistently reveal a complex pattern of entanglement. In the sub-volume-law phase, on the other hand, the entanglement spectrum statistics is no longer universal, entanglement fluctuations are larger and exhibiting a nonuniversal scaling, and the efficiency of the disentangling algorithm becomes finite. Our results, based on model wavefunctions, suggest that a similar combination of entanglement scaling properties and of entanglement complexity features may be found in high-energy Hamiltonian eigenstates---a very strong candidate being offered by the many-body localization transition of disordered lattice-spin models.

The effect of surface nucleation modulation on the mechanical and biocompatibility of metal-polymer biomaterials.

The deployment of hernia repair patches in laparoscopic procedures is gradually increasing. In this technology, however, understanding the new phases of titanium from the parent phase on polymer substrates is essential to control the microstructural transition and material properties. It remains a challenging area of condensed matter physics to predict the kinetic and thermodynamic properties of metals on polymer substrates from the molecular scale due to the lack of understanding of the properties of the metal-polymer interface. However, this paper revealed the mechanism of nucleation on polymer substrates and proposed for the first record a time-dependent regulatory mechanism for the polymer-titanium interface. The interconnection between polymer surface chain entanglement, nucleation and growth patterns, crystal structure and surface roughness were effectively unified. The secondary regulation of mechanical properties was accomplished simultaneously to satisfy the requirement of biocompatibility. Titaniumized polypropylene patches prepared by time-dependent magnetron sputtering technology demonstrated excellent interfacial mechanical properties and biocompatibility. In addition, modulation by low-temperature plasma metal deposition opened a new pathway for biomaterials. This paper provides a solid theoretical basis for the research of titanium nanofilms on medical polypropylene substrates and the medical industry of implantable biomaterials, which will be of great value in the future.

Entanglement links and the quasiparticle picture

The time evolution of a quantum state with short-range correlations after a quench to a one-dimensional critical Hamiltonian can be understood using the quasi-particle picture, which states that local entanglement spreads as if it was carried by quasi-particles which separate at a fixed speed. We extend the quasi-particle picture using the recently introduced link representation of entanglement, allowing us to apply it to initial states presenting long-range correlations. The entanglement links are current correlators, and therefore follow a wave equation on the appropriate configurational space which allows us to predict the time evolution of the entanglement entropies. Our results are checked numerically for free fermionic chains with different initial entanglement patterns.

Classification of four-qubit entangled states via machine learning

We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) to identify entanglement patterns in families of four-qubit states. The effectiveness of SVM for practical EW implementations stems from the coarse-grained description of families of equivalent entangled quantum states. The equivalence criteria in our work is based on the stochastic local operations and classical communication classification and the description of the four-qubit entangled Werner states. We numerically verify that the SVM approach provides an effective tool to address the entanglement witness problem when the coarse-grained description of a given family state is available. We also discuss and demonstrate the efficiency of nonlinear kernel SVM methods as applied to four-qubit entangled state classification.

Remotely Controlled Entanglement Generation

We consider a system of multiple qubits without any quantum control. We show that one can mediate entanglement between different subsystems in a controlled way by adding a (locally) controlled auxiliary system of the same size that couples via an always-on, distant dependent interaction to the system qubits. Solely by changing the internal state of the control system, one can selectively couple it to selected qubits, and ultimately generate different kinds of entanglement within the system. This provides an alternative way for quantum control and quantum gates that does not rely on the ability to switch interactions on and off at will, and can serve as a locally controlled quantum switch where all entanglement patterns can be created. We demonstrate that such an approach also offers an increased error tolerance w.r.t. position fluctuations.

Photon pair generation from lithium niobate metasurface with tunable spatial entanglement [Invited

The two-photon state with spatial entanglement is an essential resource for testing fundamental laws of quantum mechanics and various quantum applications. Its creation typically relies on spontaneous parametric downconversion in bulky nonlinear crystals where the tunability of spatial entanglement is limited. Here, we predict that ultrathin nonlinear lithium niobate metasurfaces can generate and diversely tune spatially entangled photon pairs. The spatial properties of photons including the emission pattern, rate, and degree of spatial entanglement are analyzed theoretically with the coupled mode theory and Schmidt decomposition method. We show that by leveraging the strong angular dispersion of the metasurface, the degree of spatial entanglement quantified by the Schmidt number can be decreased or increased by changing the pump laser wavelength and a Gaussian beam size. This flexibility can facilitate diverse quantum applications of entangled photon states generated from nonlinear metasurfaces.

Disentangled Representation Learning for Recommendation.

There exist complex interactions among a large number of latent factors behind the decision making processes of different individuals, which drive the various user behavior patterns in recommender systems. These factors hidden in those diverse behaviors demonstrate highly entangled patterns, covering from high-level user intentions to low-level individual preferences. Uncovering the disentanglement of these latent factors can benefit in enhanced robustness, interpretability, and controllability during representation learning for recommendation. However, the large degree of entanglement within latent factors poses great challenges for learning representations that disentangle them, and remains largely unexplored in literature. In this paper, we present the SEMantic MACRo-mIcro Disentangled Variational Auto-Encoder (SEM-MacridVAE) model for learning disentangled representations from user behaviors, taking item semantic information into account. Our SEM-MacridVAE model achieves macro disentanglement by inferring the high-level concepts associated with user intentions (e.g., to buy a pair of shoes or a laptop) through a prototype routing mechanism, as well as capturing the individual preferences with respect to different concepts separately. The micro disentanglement is guaranteed through a micro-disentanglement regularizer stemming from an information-theoretic interpretation of VAEs, which forces each dimension of the representations to independently reflect an isolated low-level factor (e.g., the size or the color of a shirt). The semantic information including visual and categorical signals extracted from candidate items is utilized to further boost the recommendation performance of the proposed SEM-MacridVAE model. Empirical experiments demonstrate that our proposed approach is able to achieve significant improvement over the state-of-the-art baselines. We also show that the learned representations are interpretable and controllable, capable of potentially leading to a new paradigm for recommendation where users have fine-grained control over some target aspects of the recommendation candidates.

Entanglement phases in large- N hybrid Brownian circuits with long-range couplings

We develop solvable models of large-$N$ hybrid quantum circuits on qubits and fermions with long-range power-law interactions and continuous local monitoring, which provide analytical access to the entanglement phase diagram and error-correcting properties of many-body entangled non-equilibrium states generated by such dynamics. In one dimension, the long-range coupling is irrelevant for $\alpha>3/2$, where $\alpha$ is the power-law exponent, and the models exhibit a conventional measurement-induced phase transition between volume- and area-law entangled phases. For $1/2<\alpha<3/2$ the long-range coupling becomes relevant, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for $\alpha<1$ the entanglement pattern receives a sub-volume correction for both area-law and volume-law phases, indicating that the phase realizes a quantum error correcting code whose code distance scales as $L^{2-2\alpha}$. While the entanglement phase diagram is the same for both the interacting qubit and fermionic hybrid Brownian circuits, we find that long-range free-fermionic circuits exhibit a distinct phase diagram with two different fractal entangled phases.

Entanglement spectrum and entropy in Floquet topological matter

Entanglement is one of the most fundamental features of quantum systems. In this work, we obtain the entanglement spectrum and entropy of Floquet noninteracting fermionic lattice models and build their connections with Floquet topological phases. Topological winding and Chern numbers are introduced to characterize the entanglement spectrum and eigenmodes. Correspondences between the spectrum and topology of entanglement Hamiltonians under periodic boundary conditions and topological edge states under open boundary conditions are further established. The theory is applied to Floquet topological insulators in different symmetry classes and spatial dimensions. Our work thus provides a useful framework for the study of rich entanglement patterns in Floquet topological matter.

The connected wedge theorem and its consequences

In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting.Our theorem generalizes the 2-to-2 connected wedge theorem proven in [3]. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.

Maximal entanglement velocity implies dual unitarity

A global quantum quench can be modeled by a quantum circuit with local unitary gates. In general, entanglement grows linearly at a rate given by entanglement velocity, which is upper bounded by the growth of the light cone. We show that the unitary interactions achieving the maximal rate must remain unitary if we exchange the space and time directions -- a property known as dual unitarity. Our results are robust: approximate maximal entanglement velocity also implies approximate dual unitarity. We further show that maximal entanglement velocity is always accompanied by a specific dynamical pattern of entanglement, which yields simpler analyses of several known exactly solvable models.

Detection of long-range entanglement in gapped quantum spin liquids by local measurements

Topological order, reflected in long range patterns of entanglement, is quantified by the topological entanglement entropy (TEE) $\gamma$. We show that for gapped quantum spin liquids (QSL) it is possible to extract $\gamma$ using two-spin local correlators. We demonstrate our method for the gapped $\mathbb{Z}_2$ Kitaev spin liquid on a honeycomb lattice with anisotropic interactions. We show that the $\gamma = \log 2$ for $\mathbb{Z}_2$ topological order can be simply extracted from local two-spin correlators across two different bonds, with an accuracy comparable or higher than the Kitaev-Preskill construction. This implies that the different superselection sectors of $\mathbb{Z}_2$ gauge theory determined by global Wilson loop operators can be fully reflected locally in the matter majorana sector.