D. S. Tasca, S. P. Walborn, F. Toscano, P. H. Souto Ribeiro
Transverse entanglement between pairs of photons can be detected through intensity correlation measurements in the near and far fields. We show theoretically and experimentally that at intermediate zones, it is also possible to detect transverse entanglement performing only intensity correlation measurements. Our results are applicable to a number of physical systems.
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Quantum entanglement associated with transverse wave vectors of down conversion photons is investigated based on the Schmidt decomposition method. We show that transverse entanglement involves two variables: orbital angular momentum and transverse frequency. We show that in the monochromatic limit high values of entanglement are closely controlled by a single parameter resulting from the competition between (transverse) momentum conservation and longitudinal phase matching. We examine the features of the Schmidt eigenmodes, and indicate how entanglement can be enhanced by suitable mode selecti…
We study the evolution of nearest-neighbor entanglement in the one dimensional Ising model with an external transverse field. The system is initialized as the so called "thermal ground state" of the pure Ising model. We analyze properties of generation of entanglement for different regions of external transverse fields. We find that the derivation of the time at which the entanglement reaches its first maximum with respect to the reciprocal transverse field has a minimum at the critical point. This is a new indicator of quantum phase transition.
We study entanglement and spin squeezing in the ground state of three qubits interacting via the transverse Ising model. We give analytical results for the entanglement and spin squeezing, and a quantitative relation between the concurrence, quantifying the entanglement of two spins, and the spin squeezing parameter, measuring the degree of squeezing. Finally, by appropriately choosing the exchange interaction and strengths of the transverse field, we propose a scheme for generating entangled W state from an unentangled initial state with all spins down.
We study the phenomena that arise in the transverse structure of electromagnetic field impinging on a linear Fabry-Perot cavity with an oscillating end mirror. We find quantum correlations among transverse modes which can be considered as a signature of their entanglement.
We show that, although the amount of mutual entanglement of photons propagating in free space is fixed, the type of correlations between the photons that determine the entanglement can dramatically change during propagation. We show that this amounts to a migration of entanglement in Hilbert space, rather than real space. For the case of spontaneous parametric down conversion, the migration of entanglement in transverse coordinates takes place from modulus to phase of the bi-photon state and back again. We propose an experiment to observe this migration in Hilbert space and to determine the fu…
In this paper, we study the entanglement between two-neighboring sites and the rest of the system in a simple quantum phase transition of 1D transverse field Ising model. We find that the entanglement shows interesting scaling and singular behavior around the critical point, and then can be use as a convenient marker for the transition point.
The efficiency of time dependent density matrix renormalization group methods is intrinsically connected with the rate of entanglement growth. We introduce a new measure of entanglement in the space of operators and show, for transverse Ising spin 1/2 chain, that the simulation of observables, contrary to simulation of typical pure quantum states, is efficient for initial local operators. For initial operators with a finite index in Majorana representation, the operator space entanglement entropy saturates with time to a level which is calculated analytically, while for initial operators with …
We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric downconversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional intensity measurements, is shown to be only able to characterize entanglement in the near and far field zones of the source. Therefore we also follow a different approach. By evaluating the first-order coherence of a subsystem of the state we can quantify its entanglement. Unlike previous measurements, which determine the Fedorov ratio via intensity correlations, ou…
We discuss mode-entangled states based on the optical transverse modes of the optical field propagating in multi-mode waveguides, which are classical analogs of the quantum entangled states. The analogs are discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on these analogs may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation and quantum communication.
We propose a scheme to explore two-photon high-dimensional entanglement associated with a transverse pattern by means of two-photon interference in a beamsplitter. We find that the topological symmetry of the angular spectrum of the two-photon state governs the nature of the two-photon interference. We prove that the anti-coalescence interference is the signature of two-photon entanglement. On the basis of this feature, we propose a special Mach-Zehnder interferometer incorporated with two spiral phase plates which can change the interference from a coalescence to an anti-coalescence type only…
Recently Seevinck and Uffink argued that genuine multipartite entanglement (GME) had not been established in the experiments designed to confirm GME. In this paper, we use the Bell-type inequalities introduced by Seevinck and Svetlichny [Phys. Rev. Lett. \textbf{89}, 060401 (2002)] to investigate the GME problem in the one-dimensional transverse-field Ising model. We show explicitly that the ground states of this model violate the inequality when the external transverse magnetic field is weak, which indicate that the ground states in this model with weak magnetic field are fully entangled. Sin…
We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A $σ_x σ_x$-type Ising interaction is realized between quantum bits stored in the ground hyperfine clock states of Yb ions. We demonstrate entangling gates and tailor the spin-spin couplings with two and three trapped ions. The use of closely-spaced transverse modes provides a new class of interactions relevant to quantum computing and simulation with large collections of ions in a single crystal.
The photon-pairs generated through spontaneous parametric down-conversion (SPDC) possess strong correlations in their transverse position and momentum degrees of freedom. For such photon pairs, the transverse position correlation length depends on the crystal thickness and the pump wavelength, whereas the transverse momentum correlation length depends on the beam waist and spatial coherence length of the pump. By controlling these parameters, it is possible to engineer the spatial entanglement. Here, we utilize the circular asymmetry of the pump by using an elliptical-Gaussian beam to change t…
We determine the conditions under which general dimer-type spin chains with $XYZ$ couplings of arbitrary range in a general transverse field will exhibit an exactly separable parity-breaking eigenstate. We also provide sufficient conditions which ensure that it will be a ground state. We then examine the exact side limits at separability of the entanglement between any two spins in a finite chain, showing that in the vicinity of separability, the system will loose all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and in…
We have designed and implemented a photon-pair source, based on the spontaneous four wave mixing (SFWM) process in a few-mode fiber, in a geometry which permits multiple, simultaneous SFWM processes, each associated with a distinct combination of transverse modes for the four participating waves. In our source: i) each process is group-velocity-matched so that it is, by design, nearly-factorable, and ii) the spectral separation between neighboring processes is greater than the marginal spectral width of each process. Consequently, there is a direct correspondence between the joint amplitude of…
We determine the conditions for the existence of non-transverse factorizing magnetic fields in general spin arrays with anisotropic XYZ couplings of arbitrary range. It is first shown that a uniform maximally aligned completely separable eigenstate can exist just for fields ${h}_s$ parallel to a principal plane and forming four straight lines in field space, with the alignment direction different from that of ${h}_s$ and determined by the anisotropy. Such state always becomes a non-degenerate ground state (GS) for sufficiently strong (yet finite) fields along these lines, in both ferromagnetic…
As known, the degree of entanglement of biphoton states with respect to the transverse components of photon wave vectors (momenta) or coordinates can be characterized either by the parameter K associated with the Schmidt decompositions, or by the parameter R, defined as the ratio of the widths of the unconditional and conditional single-particle distributions of biphoton states. As entanglement is a fundamental characteristics of a state, it must be independent of a choice of its different representations, i.e. its entanglement parameters must be identical in the coordinate and momentum repres…
A key ingredient in emerging quantum-enhanced technologies is the ability to coherently manipulate and detect superpositions of basis states. In integrated optics implementations, transverse spatial modes supported by multimode structures offer an attractive carrier of quantum superpositions. Here we propose an integrated dynamic mode converter based on the electro-optic effect in nonlinear channel waveguides for deterministic transformations between mutually non-orthogonal bases of spatial modes. We theoretically show its capability to demonstrate a violation of a Bell-type Clauser-Horne-Shim…
We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through $XYZ$ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the r…
Conditional interference patterns can be obtained with twin photons from spontaneous parametric down-conversion and the phase of the pattern can be controlled by the relative transverse position of the signal and idler detectors. Using a configuration that produces entangled photons in both polarization and transverse momentum we report on the control of the conditional patterns by acting on the polarization degree of freedom.
The quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model in a transverse magnetic field is studied in this paper. An exact solution is obtained by using an extended Jordan and Wigner transformation to the pseudo-spin operators. The fidelity susceptibility, the concurrence, the block-block entanglement entropy, and the pseudo-spin correlation functions are calculated with antiperiodic boundary conditions. The QPT driven by the transverse field only emerges at zero field and is of the second-order. Several critical exponents obtained by finite size scaling analysis ar…
The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement entropy always scales linearly with the block size. However, besides this \emph{area law} contribution, we find a subleading logarithmic correction at the quantum critical point. This correction is discussed from the point of view of an underlying percolation transition, both at finite and at zero temperature.
In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two and three dimensions from a multi-partite entanglement point of view. Using \emph{exact} numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric GHZ-like state to a paramagnetic product-state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling b…
Robust detection of an entanglement transition in the projective transverse field Ising model
该研究提出了一种结合错误校正与经典影子态重构的方法，在投影横向磁场伊辛模型中实现对纠缠相变的稳健检测。
Numerical results for the concurrence and bounds on the localizable entanglement are obtained for the square lattice spin-1/2 XXZ-model and the transverse field Ising-model at low temperatures using quantum Monte Carlo.
Discrete quantum trajectories of systems under random unitary gates and projective measurements have been shown to feature transitions in the entanglement scaling that are not encoded in the density matrix. In this paper, we study the projective transverse field Ising model, a stochastic model with two noncommuting projective measurements and no unitary dynamics. We numerically demonstrate that their competition drives an entanglement transition between two distinct steady states that both exhibit area law entanglement, and introduce a classical but nonlocal model that captures the entanglemen…
Entanglement Phase Transition in Chaotic non-Hermitian Systems
研究非厄运混沌自旋链中的纠缠相变，通过分析复杂谱发现两种模型在临界阈值后经历耗散诱导的无隙到有隙相变，并揭示复杂隙与纠缠熵的非单调行为。
The orbital angular momentum of light (OAM) provides a promising approach for the implementation of multidimensional states (qudits) for quantum information purposes. In order to characterize the degradation undergone by the information content of qubits encoded in a bidimensional subspace of the orbital angular momentum degree of freedom of photons, we study how the state fidelity is affected by a transverse obstruction placed along the propagation direction of the light beam. Emphasis is placed on the effects of planar and radial hard-edged aperture functions on the state fidelity of Laguerr…
We produce polarization entangled states with variable degree of entanglement for twin photons. Entanglement in polarization is coupled to entanglement in position that produces transverse coincidence interference fringes. We show both theoretically and experimentally that, due to this coupling, we can use the interference pattern to measure the polarization degree of entanglement.
The entanglement entropy of the random transverse-field Ising model is calculated by a numerical implementation of the asymptotically exact strong disorder renormalization group method in 2d, 3d and 4d hypercubic lattices for different shapes of the subregion. We find that the area law is always satisfied, but there are analytic corrections due to E-dimensional edges (1<=E<=d-2). More interesting is the contribution arising from corners, which is logarithmically divergent at the critical point and its prefactor in a given dimension is universal, i.e. independent of the form of disorder.
We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and L=2. In the general case, the critical entropy is shown to be additive when d goes to infinity. Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d. This formula is in excellent agreement with nu…
Separation between Entanglement Criteria and Entanglement Detection Protocols
本文通过提出EDP公设并分析未知纯双体态检测任务，证明纠缠判据的可观测量数量与EDP样本复杂度可指数分离，凸显EDP独立设计价值。
We compute concurrence and negativity as measures of two-site entanglement generated by a power-law quench (characterized by a rate 1/tau and an exponent alpha) which takes an anisotropic XY chain in a transverse field through a quantum critical point (QCP). We show that only the even-neighbor pairs of sites get entangled in such a process. Moreover, there is a critical rate of quench, 1/tau_c, above which no two-site entanglement is generated; the entire entanglement is multipartite. The ratio of the two-site entanglements between consecutive even neighbors can be tuned by changing the quench…
Integrated entangled photon pair source is an essential resource for both fundamental investigations and practical applications of quantum information science. Currently there have been several types of entanglement, among which the transverse-mode entanglement is becoming attractive because of its unique advantages. Here, we report an on-chip transverse-mode entangled photon pair source via the spontaneous four-wave mixing processes in a multimode silicon waveguide. Transverse-mode photon pairs are verified over multiple frequency channels within a bandwidth of $\sim$2~THz, and a maximally en…
Entanglement has developed into an essential concept for the characterization of phases and phase transitions in ground states of quantum many-body systems. In this work, we use the logarithmic negativity to study the spatial entanglement structure in the transverse-field Ising chain both in the ground state and at nonzero temperatures. Specifically, we investigate the entanglement between two disjoint blocks as a function of their separation, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond wh…
Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (eLOCC) are studied. We propose a new method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground state local convertibility in the one dimensional transverse field Ising model, XY model and XXZ model. It is found that the eLOCC convertibility sudden changes at the phase transition points. In transverse field Ising model the eLOCC convertibility between the first excited state and the g…
The non-equilibrium evolution of the block entanglement entropy is investigated in the XY chain in a transverse magnetic field after the Hamiltonian parameters are suddenly changed from and to arbitrary values. Using Toeplitz matrix representation and multidimensional phase methods, we provide analytic results for large blocks and for all times, showing explicitly the linear growth in time followed by saturation. The consequences of these analytic results are discussed and the effects of a finite block length is taken into account numerically.
Entanglement certification in bulk nonlinear crystals for degenerate and non-degenerate SPDC: spectral filter effects on transverse spatial correlations
研究了非线性晶体中退相干和非退相干SPDC过程的频谱滤波对横纵空间相关性的影响，发现远场中退相干条件的动量宽度受泵浦限制，而非退相干条件的动量宽度随带宽增加而单调增长，且走偏轴对动量宽度的敏感性远高于非走偏轴。
I exploit the formal equivalence between the ground state of a $d$ dimensional quantum system and a d+1 dimensional classical Ising chain to represent quantum entanglement in terms of classical correlations only. This offers a general "local hidden variable model" for all quantum phenomena existing in one dimension lower than the (hidden variable) classical model itself. The local hidden variable model is not contradicted by the implications of Bell's theorem. Formal theory is presented first and then exemplified by the quantum Ising spin chain in a transverse magnetic field. Here I explicitel…
We provide a study of various quantum phase transitions occurring in the XY Heisenberg chain in a transverse magnetic field using the Meyer-Wallach (MW) measure of (global) entanglement. Such a measure, while being readily evaluated, is a multipartite measure of entanglement as opposed to more commonly used bipartite measures. Consequently, we obtain analytic expression of the measure for finite-size systems and show that it can be used to obtain critical exponents via finite-size scaling with great accuracy for the Ising universality class. We also calculate an analytic expression for the iso…
We analyze the entanglement measure $C_4$ for mixed states in general and for the transverse XY model. We come to the conclusion that it cannot serve alone for guaranteeing an entanglement of $GHZ_4$-type. The genuine negativity calculated in Ref.~\cite{Hofmann14} isn't sufficient for that either and some additional measure of entanglement must be considered. In particular we study the transverse XY-model and find a non-zero $C_4$ measure which is of the same order of magnitude than the genuine negativity. Furthermore, we observe a feature in the $C_4$ values that resembles a destructive inter…
Witness based nonlinear detection of quantum entanglement
提出非线性纠缠检测策略，利用多份拷贝及见证者与可观测量结合，检测线性策略及见证者单独无法检测的纠缠，并推广至多分纠缠与纠缠浓缩。
A Study of Entanglement and Ansatz Expressivity for the Transverse-Field Ising Model using Variational Quantum Eigensolver
本文利用VQE算法研究横向场异斯模型中的纠缠与ansatz表达性，通过不同ansatz评估其在多体系统中的性能。
We consider the time evolution of the gaps of the entanglement spectrum for a block of consecutive sites in finite transverse field Ising chains after sudden quenches of the magnetic field. We provide numerical evidence that, whenever we quench at or across the quantum critical point, the time evolution of the ratios of these gaps allows to obtain universal information. They encode the low-lying gaps of the conformal spectrum of the Ising boundary conformal field theory describing the spatial bipartition within the imaginary time path integral approach to global quenches at the quantum critica…
Entanglement detection length of multipartite quantum states
本文提出纠缠检测长度概念，刻画检测真正多体纠缠所需联合测量的最少粒子数，并利用边际态可分性检验和半定规划方法给出确定方式与上界。
Thermal quantum correlations of a single electron in a double quantum dot with transverse magnetic field
本文研究了半导体双量子点中单电子在磁场下的热量子关联，推导了热并发性和相关相干性的解析表达式，发现横向磁场可调节系统纠缠与相干性，且相关相干性比纠缠更稳健，为量子算法设计提供了依据。
Emergence of Strategic Equilibria from Transverse Field Ising Hamiltonian Dynamics
该研究基于横向场伊辛哈密顿量动力学，提出算子形式的量子博弈研究方法，通过可调纠缠算子解决博弈困境，获得优于经典结果的量子优势，为量子博弈设计提供硬件相关视角。
Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example.
In this paper we investigate the relationship between direct-sum majorization formulation of uncertainty relations and entanglement, for the case of two and many observables. Our primary results are entanglement detection methods based on direct-sum majorization uncertainty relations. These nonlinear detectors provide a set of necessary conditions for detecting entanglement whose number grows with the dimension of the state being detected.
A probability density characterization of multipartite entanglement is tested on the one-dimensional quantum Ising model in a transverse field. The average and second moment of the probability distribution are numerically shown to be good indicators of the quantum phase transition. We comment on multipartite entanglement generation at a quantum phase transition.
withdrawn by the authors because of an error.
Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of a mixed-species ion chain for entangling operations and also sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at leas…
Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations, the violation of which would imply entanglement. Corollaries to these theorems yield infinite sets of scalar entanglement detection criteria based on quasi-entropic measures of disorder. Examples are analyzed to probe the efficacy of the derived criteria in detecting the entanglement of bipartite Werner states. Characteristics of the majorization relation as a…
Bound entanglement detection in $4 \otimes 4$ systems via generalized Choi maps
本文提出一种正但不完全正线性映射，用于高维量子系统中束缚纠缠的检测。
Witnessing entanglement is crucial in quantum information processing. With properly preparing ancillary states, it has been shown previously that genuine entanglement can be witnessed without trusting measurement devices. In this work, we generalize the scenario and show that generic multipartite entanglement structures, including entanglement of subsystems and entanglement depth, can be witnessed via measurement-device-independent means. As the original measurement-device-independent entanglement witness scheme exploits only one out of four Bell measurement outcomes for each party, a direct g…
We have studied the concurrence of two-site entanglement and have shown that it is related to the geometric phase accumulated due to a complete rotation of the entangled state. The geometric phase and hence the concurrence is evaluated for transverse Ising model and antiferromagnetic chain which is found to be in good agreement with that obtained by other methods.
We investigate the generation of entanglement in systems of identical fermions through a process involving particle detection, focusing on the implications that this kind of processes have for the concept of entanglement between fermionic particles. As a paradigmatic example we discuss in detail a scheme based on a splitting-plus-detection operation. This scheme generates states with accessible entanglement starting from an initial pure state of two indistinguishable fermions exhibiting correlations due purely to antisymmetrization. It is argued that the proposed extraction of entanglement doe…
Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantity the entanglement depth of many-body systems and is easy to implement as it requires to measure only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially …
A note on entanglement detection via the generalized realignment moments
本文提出基于广义重排矩的两个分离性判据，通过引入额外参数提升判据的灵活性和强度，并通过实例验证其在纠缠检测中的有效性。
We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability.
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