Local Entanglement Research Articles

Distillation of lossy hyperentangled states

Hyperentanglement has a higher information density than conventional single-degree-of-freedom entanglement, which has attracted much attention due to its fascinating applications in quantum communication. However, since the inevitable interactions between quantum entangled systems and the environment will drive hyperentangled systems into less hyperentangled states or even mixed hyperentangled states, the efficiency and security of quantum communication will be greatly depressed. The currently existing distillation protocols are not universal, i.e., they only work for the lossy hyperentangled states in specific systems. In this paper, based on local positive-operator-valued measures (POVMs), we present a distillation protocol for lossy hyperentangled photonic Bell and Greenberger-Horne-Zeilinger (GHZ) states. The intrinsic property of our protocol is twofold, i.e., the POVM nature of the protocol guarantees that the protocol is a universal one, and the distillation operation on only one of the two degrees of freedom (DOFs) can enhance the fidelity of the system in both DOFs. Furthermore, in the implementation level, our hyperentanglement distillation protocol (HEDP) has other two merits: no auxiliary local entanglement resources and sophisticated single-photon detectors are required, and only one copy of the lossy state will be operated in each distillation round, which show that our HEDPs are relatively simple and feasible.

Hierarchy of Linear Light Cones with Long-Range Interactions

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute -- given a many-body state, $\mathcal{O}_x(t) \mathcal{O}_y |\psi\rangle \approx \mathcal{O}_y\mathcal{O}_x(t) |\psi\rangle$ with arbitrarily small errors -- so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance $r$ interact with potential energy $V(r) \propto 1/r^{\alpha}$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, this linear light cone exists for every many-body state when $\alpha>3$ (Lieb-Robinson light cone); for a typical state chosen uniformly at random from the Hilbert space when $\alpha>\frac{5}{2}$ (Frobenius light cone); for every state of a non-interacting system when $\alpha>2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones -- and their tightness -- also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

Experimental simulation of the four-dimensional Yang-Baxter equation on a spin quantum simulator

The Yang-Baxter equation (YBE) has created many applications in the integrable models of the statistical mechanics. It is recently shown that the YBE can be further applied in quantum information processing. Conversely, quantum simulation also provides novel approaches for effectively checking the YBE in quantum devices. Here, we adopted the method inspired by the previous work to experimentally perform the simulation of the YBE on a four-qubit nuclear magnetic resonance quantum processor. Whether the YBE is satisfied or not can be preliminarily determined by measuring the ancillary qubit without the assistance of quantum state tomography, and two hand sides of the YBE are concurrently simulated, not in separate forms involved in the existing protocols. The experimental result shows that the discrimination accuracy is over 98.1% when the condition of YBE is satisfied. The global and local entanglements in the YBE system are also studied by the numerical simulation and experiments. It is found that the YBE is not only a tool to yield the global entanglement but also the symptom when the local entanglement is equal to each other.

Extremal photon statistics signal the extremal entanglement

Entanglement and photon statistics are investigated in a cavity QED system with three two-level atoms trapped in a modestly driven cavity with weak dissipation. It is shown that the local maximal steady-state entanglement of any two atoms perfectly corresponds to the strongest photon antibunching point. In particular, the local maximal entanglement of two atoms is also consistent with the strongest photon bunching point. It provides a new angle to understand both photon statistics and entanglement. Our work gives strong support for employing extremal photon statistics to signal the extremal atomic entanglement in this system.

Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

We study an effective spin model derived perturbatively from random transverse-field Ising model on the pyrochlore lattice. The model consists of spin-configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization upto N=64 site systems. We calculate spin-glass correlation functions and local entanglement entropy $S_T$ between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where $S_T=\ln{6}$. Increasing randomness first leads to a frozen phase, with long-range spin-glass order and $S_T=\ln{2}$ corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

I am becoming my mother: (post)diaspora, local entanglements and entangled locals

ABSTRACTDrawing on the sensory, self-shifting approach of Lorna Goodison’s 1986 poem ‘I am becoming my mother’, and on quantum theory for brief insights into entanglement, this article gazes into the still visualities of family photographs of my own Birmingham childhood (my mother died that same year) to push towards a more entangled conception of (post)diaspora. I use this highly personal entanglement to take issue with three troublingly disentangled ways in which postdiaspora has been imagined in recent academic literature: as the culmination of a teleological movement from migrant to diaspora to post-diaspora; as the slowly weakening pull of diasporic responsibilities and remittances; and as a means to archaise and de-link from ties to a forgetful and irresponsible diaspora. Ultimately, the article pushes towards a more deeply materially and personally entangled version of (post)diaspora.

Many-body localization with synthetic gauge fields in disordered Hubbard chains

We analyze the localization properties of the disordered Hubbard model in the presence of a synthetic magnetic field. An analysis of level spacing ratios shows a clear transition from ergodic to many-body localized phase. The transition shifts to larger disorder strengths with increasing magnetic flux. Study of dynamics of local correlations and entanglement entropy indicates that charge excitations remain localized whereas spin degree of freedom gets delocalized in the presence of the synthetic flux. This residual ergodicity is enhanced by the presence of the magnetic field with dynamical observables suggesting incomplete localization at large disorder strengths. Furthermore, we examine the effect of quantum statistics on the local correlations and show that the long-time spin oscillations of a hard-core boson system are destroyed as opposed to the fermionic case.

Design and experimental performance of local entanglement witness operators

Entanglement is a central concept in quantum information and a key resource for many quantum protocols. In this work we propose and analyze a class of entanglement witnesses that detect the presence of entanglement in subsystems of experimental multi-qubit stabilizer states. The witnesses we propose can be decomposed into sums of Pauli operators and can be efficiently evaluated by either two measurement settings only or at most a number of measurements that only depends on the size of the subsystem of interest. We provide two constructive methods to design the local witness operators, the first one based on the local unitary equivalence between graph and stabilizer states, and the second one based on sufficient and necessary conditions that the respective set of constituent Pauli operators needs to fulfill. We theoretically establish the noise tolerance of the proposed witnesses and benchmark their practical performance by analyzing the local entanglement structure of an experimental seven-qubit quantum error correction code.

Rum Runners of the Baltic—The Rise of Transnational Liquor Smuggling Networks in Interwar Europe

This article analyzes the local and transnational entanglements of interwar liquor contraband operations to show how smuggling in the Baltic Sea region grew from small-scale coast-to-coast operations to a large-scale trade organized by transnational syndicates moving millions of liters. It examines transnational smuggling networks, the use of flags of convenience and large base ships to argue that the framework of the “Helsinki Convention for the Suppression of the Contraband Traffic in Alcoholic Liquors of 1925” led to professionalization and trans-nationalization of contraband operations and a significant growth in liquor smuggling. The analysis of the Free City of Danzig, where the boundaries between small-scale smuggling and professional contraband operations were fluid, provides insights into the local elements of liquor smuggling operations. This part of the argument focuses on the weak governmental control and the tax-free area in the Danzig port, which provided the necessary infrastructure for large-scale smuggling and enabled the city-state to become a major hub for liquor smuggling operations.

Local entanglement and confinement transitions in the random transverse-field Ising model on the pyrochlore lattice

We use numerical linked cluster expansions (NLC) and exact diagonalization to study confinement transitions out of the quantum spin liquid phase in the pyrochlore-lattice Ising antiferromagnet with random transverse fields. We calculate entanglement entropies associated with local regions defined by single tetrahedron to observe these transitions. The randomness-induced confinement transition is marked by a sharp reduction in the local entanglement and a concomitant increase in Ising correlations. In NLC, it is studied through the destruction of loop resonances due to random transverse-fields. The confining phase is characterized by a distribution of local entanglement entropies, which persists to large random fields.

Local entanglement and string order parameter in dimerized models

In this letter, we propose an application of string order parameter (SOP), commonly used in quantum spin systems, to identify symmetry-protected topological phase (SPT) in fermionic systems in the example of the dimerized fermionic chain. As a generalized form of dimerized model, we consider a one-dimensional spin-1/2 XX model with alternating spin couplings. We employ Jordan–Wigner fermionization to map this model to the spinless Su–Schrieffer–Heeger fermionic model (SSH) with generalized hopping signs. We demonstrate a phase transition between a trivial insulating phase and the Haldane phase by the exact analytical evaluation of reconstructed SOPs which are represented as determinants of Toeplitz matrices with the given generating functions. To get more insight into the topological quantum phase transition (tQPT) and microscopic correlations, we study the pairwise concurrence as a local entanglement measure of the model. We show that the first derivative of the concurrence has a non-analytic behaviour in the vicinity of the tQPT, like in the second order trivial QPTs.

Microwave assisted sinter molding of polyetherimide/carbon nanotubes composites with segregated structure for high-performance EMI shielding applications

The formation of segregated conductive structure in a polymer matrix can remarkably improve the electrical and EMI shielding performance. Nevertheless, the insufficient interfacial bonding force among polymer domains generated during the conventional hot compressing process will seriously deteriorate the mechanical property of the final composite. Herein, high-performance polyetherimide/carbon nanotubes (PEI/CNTs) composites with segregated structure were facilely fabricated for EMI shielding applications using CNTs as both solder and a conductive framework. The surface-localized CNTs were selectively and vigorously heated upon exposure to microwave (MW) irradiation, with an appropriate pressure stress applied subsequently, ensuring enhanced local polymer mobility and entanglement across the interfacial regions. Consequently, an excellent conductivity and EMI shielding effectiveness (EMI SE) of 17.98 S/m and 34.6 dB, respectively, at 8.2–12.4 GHz were achieved in the PEI/CNTs composites only employing 4.0 wt% CNTs, along with the tensile strength of ~36 MPa, due to the superb welding induced by the MW selective sintering. All the results indicated that this effort provided a novel, economical and easily industrialized concept for fabricating segregated high-performance polymer composites for EMI shielding applications.

Quantum Entanglement in Ground State of Extended Hubbard Model

Metal-insulator and CDW-SDW transitions are studied in the one-dimensional Extended Hubbard Model at half-filling by analysing the behaviour of local entanglement in fermionic systems. 1D traditional Hubbard model exhibits metal-insulator transition at critical point Uc = 0, where local entanglement reaches its maximum value. Moreover, a transition between charge- and spin-density- wave (CDW-SDW) occurs in 1D Extended Hubbard Model tUV with long-range interaction at straight line U = 2 V. The analysis of our obtained results shows that CDW-SDW transition has curious properties whose can be used in quantum information processing.

Tuning the thermal entanglement in a Ising-XXZ diamond chain with two impurities

We study the local thermal entanglement in a spin-1/2 Ising-XXZ diamond structure with two impurities. In this spin chain, we have two impurities with an isolated XXZ dimer between them. We focus on the study of the thermal entanglement in this dimer. The main goal of this paper is to provide a good understanding of the effect of impurities in the entanglement of the model. This model is exactly solved by a rigorous treatment based on the transfer-matrix method. Our results show that the entanglement can be tuned by varying the impurities parameters in this system. In addition, it is shown that the thermal entanglement for such a model exhibits a clear performance improvement when we control and manipulate the impurities compared to the original model without impurities. Finally, the impurities can be manipulated to locally control the thermal entanglement, unlike the original model where it is done globally.

Local Entanglement Entropy and Mutual Information across the Mott Transition in the Two-Dimensional Hubbard Model.

Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the Mott transition in the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory, and focus on two key measures of quantum correlations: entanglement entropy and a measure of total mutual information. We show that they detect the first-order nature of the transition, the universality class of the end point, and the crossover emanating from the end point.

Quantum Phase Transition for One-Dimensional Spin-1 XXZ Model with Uniaxial Single-Ion-Type Anisotropy

The quantum phase transitions for one-dimensional spin-1 XXZ model with uniaxial single-ion-type anisotropy are investigated by numerical simulation. The Gaussion transition occurred between the Larged-D phase and Neel phase, which is a gapped phase. The results of ground state energy, local order parameter and entanglement entropy agree with each other. The figures for all of the physical observable are shown in the text.

Recovery of nonseparability in self-healing vector Bessel beams

One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle both, classically and in the quantum regime. Here we demonstrate that the local entanglement, or non-separability, between the spatial and polarisation degrees of freedom also experience self-healing. We measured and quantified the degree of non-separability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of non-separability reduces after the obstruction, it recovers to its maximum value within the classical self-healing distance. To confirm our findings, we performed a Clauser-Horne-Shimony-Holt Bell-like inequality measurement, proving the self-reconstruction of non-separability. These results indicate that local entanglement between internal degrees of freedom of a photon, can be recovered by suitable choice of the enveloping wave function.

Correlations in local measurements and entanglement in many-body systems

While entanglement plays an important role in characterizing quantum many-body systems, it is hardly possible to directly access many-body entanglement in real experiments. In this paper, we study how bipartite entanglement of many-body states is manifested in the correlation of local measurement outcomes. In particular, we consider a measure of correlation defined as the statistical distance between the joint probability distribution of local measurement outcomes and the product of its marginal distributions. Various bounds of this measure are obtained and several examples of many-body states are considered as a testbed for the measure. We also generalize the framework to the case of imprecise measurement and argue that the considered measure is related to the concept of quantum macroscopicity.

Maximally entangled state and Bell’s inequality in qubits

A maximally entangled state is a quantum state which has maximum von Neumann entropy for each bipartition. Through proposing a new method to classify quantum states by using concurrences of pure states of a region, one can apply Bell’s inequality to study intensity of quantum entanglement of maximally entangled states. We use a class of seven-qubit quantum states to demonstrate the method, in which we express all coefficients of the quantum states in terms of concurrences of pure states of a region. When a critical point of an upper bound of Bell’s inequality occurs in our quantum states, one of the quantum state is a ground state of the toric code model on a disk manifold. Our result also implies that the maximally entangled states do not suggest local maximum quantum entanglement in our quantum states.

Love is Love

Trinidad and Tobago’s anti-gay laws can be traced back to British colonialism and European imperialism. Their existence today and their consequences for human lives in Trinidad and Tobago during the past one hundred years are a local entanglement of historic global hierarchies of power. On 12 April 2018, in the High Court of Port of Spain, capital of Trinidad and Tobago, Justice Devindra Rampersad, in a form of judicial activism, trod where local politicians have not dared and intervened in such coloniality by delivering a legal judgement upholding the challenge by Jason Jones to the nineteenth-century colonial laws in Trinidad and Tobago that criminalise homosexual relations and same-sex loving.