Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures

Four-qubit entanglement has been investigated using a recent proposed entanglement measure, multiple entropy measures （MEMS）. We have performed optimization for the nine different families of states of four-qubit system. Some extremal entangled states have been found.     

Entanglement versus bell violations and their behavior under local filtering operations

We discuss the relations between the violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for systems of two qubits on the one side and entanglement of formation, local filtering operations, and the entropy and purity on the other. We calculate the extremal Bell violations for a given amount of entanglement of formation and characterize the respective states, which turn out to have extremal properties also with respect to the entropy, purity, and several entanglement monotones. The optimal local filtering operations leading to the maximal Bell violation for a given state are provided, and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed.     

Intrinsic states in atomic shell theory

The use of intrinsic states to resolve multiplicity difficulties in nuclear shell theory has been extended to the atomic case. If Slater determinantal product states are cast in the role of intrinsic states, it is often possible to produce final states that approximate to the physical states better than those determined by the group-theoretical procedures of Racah. The standard multiplicity separations for electrons of various azimuthal quantum numbersl can also be reproduced in many cases by a judicious choice of an intrinsic state. The usefulness of the method is limited principally by the fact that orthogonal intrinsic states do not necessarily yield orthogonal final states.     

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.     

两态和三态多体纯态的度量和分类

基于多体纯态纠缠的度量方法，研究了两态两体和三体以及三态两体纯态纠缠的分类和度量.结果表明，在随机局域操作与经典通信(SLOCC)等价的意义下，纯态的纠缠方式可用所定义纠缠度的不同极大值来表征.通过仔细的计算和分析发现，两态三体和三态两体纯态各有三种SLOCC不等价的基本纠缠方式.最后将三态两体纯态纠缠度的计算与新近提出的熵积纠缠度方案进行了比较，并进行了讨论. 关键词： 纯态纠缠 极值纠缠 随机局域操作和经典通信     

Covariant holographic entanglement negativity

We propose a covariant holographic conjecture for the entanglement negativity of bipartite mixed states in \((1+1)\)-dimensional conformal field theories dual to bulk non static \(AdS_{3}\) configurations. Application of our conjecture to \((1+1)\)-dimensional conformal field theories dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduce the corresponding entanglement negativity obtained through the replica technique, in the large central charge limit. We briefly discuss the issue of the generalization of our conjecture to higher dimensions.     

Quantification of Entanglement Entropy in Helium by the Schmidt–Slater Decomposition Method

In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns ¹ S ^e states (with n = 1 to 6) and triplet-spin 1sns ³ S ^e states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt–Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.     

The electronic structure of hydrogen fluoride

Self-consistent field (SCF) calculations have been carried out for hydrogen fluoride at the experimental internuclear distance using a single determinantal wave function composed of molecular orbitals (MO's) expressed as linear combinations of atomic orbitals (LCAO's). The AO's used are of Slater-type in which the parameters have been varied within the framework of the variational method. The improvement in the energy and other physical quantities brought about by the variation of the Slater parameters has been discussed in relation to the results of other methods of obtaining improved wave functions for this molecule.     

The Structure of State Space with Respect to Imbedding

The entanglement of formation as well as the conditional entropy can be used to define leaves in the state space, given by the linear superposition of their extremal points. Examples, where these leaves can be found and can be used to calculate the entanglement respectively the conditional entropy are presented. The definition of entanglement is generalized to infinite systems and allows again to find a leaf structure. Finally we remark on the additivity property of both expressions, offering a counter example to the additivity of the conditional entropy.     

Entanglement Dynamics and Transfer for Two-Qubit Werner-Like States in Markovian Environments

We investigate entanglement dynamics and transfer in a system of two identical independent qubits, each of them locally interacting with a bosonic reservoir. Starting from two-qubit extended Werner-like states, we have shown that the degree of entanglement of the initial states, Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs’ entanglement sudden birth. Moreover, the phenomenon of entanglement sudden death/birth may occur depending on the values of parameters like purity or degree of entanglement of the initial state. When initial states are not pure, entanglement sudden death/birth always occurs, this will permit us to link the occurrence time of entanglement sudden death/birth and entanglement transfer to the purity or the degree of entanglement of the initial states.     

Creation of Entanglement with Nonlocal Operations

We discuss how to create more entanglement with nonlocal operations acting on two-particle states. For a given nonlocal operation, we find that some input states cannot produce entanglement and some produce the maximal entanglement, and find that any initial entangled states can produce more entanglement than initial product states.     

Creation of Entanglement with Nonlocal Operations

We discuss how to create more entanglement with nonlocal operations acting on two-particle states. For a given nonlocal operation, we find that some input states cannot produce entanglement and some produce the maximal entanglement, and find that any initial entangled states can produce more entanglement than initial product states.     

Dynamics of Entanglement of Qutrit-Qutrit States with Stochastic Dephasing

The effect of stochastic dephasing on the dynamics of entanglement of qutrit-qutrit states is investigated by using negativity and bound entanglement defined with realignment criterion. From the analysis, we find that the time evolution of quantum free entanglement and bound entanglement depends on the fluctuations of the stochastic variables and the parameters of the particular initial states of concern. Our results imply that some qutrits states display both distillability sudden death and entanglement sudden death, while some states do not display distillability sudden death but onlyentanglement sudden death.     

Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.     

Dynamical Creation of Entanglement and Steady Entanglement Between Two Spatially Separated Λ-Type Atoms

We report possibility of generating entanglement and steady entanglement between two identical atoms in free space with a very natural way when their spatial separation is on the order of wavelength or less. We show a dynamical creation of entanglement and steady entanglement due to the radiative coupling with different separable initial atomic states and study the entanglement properties about this atomic subsystem. Not only the creation of steady state entanglement is decided by the initial atomic states, but also the magnitude of the entanglement and the steady state entanglement are found to be strongly dependent on the initial states. We derive a master equation for the atomic subspace and solve it analytically to show how the spontaneous emission from the two atoms system induces entanglement and steady entanglement, the crossing coupling terms in master equation can enhance the entanglement value.     

Two remarks on extremal equilibrium states

First it is shown that each extremal equilibrium state is representable as limit of Gibbs states in finite volumes, and that an analogous statement holds for extremal invariant equilibrium states. Secondly we prove that for negative pair interactions only one equilibrium state exists which minimizes (resp. maximizes) the particle density, but that in general there are more than two extremal invariant equilibrium states with the same particle density. In this context, periodic interactions are studied.     

Quantum entanglement in a soluble two-electron model atom

We investigate the entanglement properties of bound states in an exactly soluble two-electron model, the Moshinsky atom. We present exact entanglement calculations for the ground, first and second excited states of the system. We find that these states become more entangled when the relative inter-particle interaction becomes stronger. As a general trend, we also observe that the entanglement of the eigenstates tends to increase with the states’ energy. There are, however, “entanglement level-crossings” where the entanglement of a state becomes larger than the entanglement of other states with higher energy. In the limit of weak interaction, we also compute (exactly) the entanglement of higher excited states. Excited states with anti-parallel spins are found to involve a considerable amount of entanglement even for an arbitrarily weak (but non zero) interaction. This minimum amount of entanglement increases monotonically with the state’s energy. Finally, the connection between entanglement and the Hartree-Fock approximation in the Moshinsky model is addressed. The quality of the ground-state Hartree-Fock approximation is shown to deteriorate, and the corresponding correlation energy to grow, as the entanglement of the (exact) ground state increases. The present work goes beyond previous related studies because we fully take into account the identical character of the two constituting particles in the entanglement calculations, and provide analytical, exact results both for the ground and the first few excited states.     

Measures of genuine multipartite entanglement for graph states

Graph states are special multipartite entangled states that have been proven useful in a variety of quantum information tasks. We address the issue of characterizing and quantifying the genuine multipartite entanglement of graph states up to eight qubits. The entanglement measures used are the geometric measure, the relative entropy of entanglement, and the logarithmic robustness, have been proved to be equal for the genuine entanglement of a graph state. We provide upper and lower bounds as well as an iterative algorithm to determine the genuine multipartite entanglement.     

Linear entropy in the Jaynes-Cummings model with a Kerr nonlinearity

The dynamical properties of quantum entanglement in the integrable Jaynes-Cummings model with a Kerr nonlinearity are studied in terms of the reduced-density linear entropy with various Kerr coupling parameters and initial states, where the initial states are prepared by the coherent states placed in the corresponding phase space described in terms of canonical variables. The mean entanglement averaged over time is employed to investigate the behavior of entanglement of those coherent states. It is shown that the mean entanglement of the coherent states put near the centers of periodic orbits, both with a strong Kerr coupling and without a Kerr coupling, tends to be the minimal, and that the mean entanglement of the coherent states centered near the boundary with a strong Kerr coupling is the minimal while that without Kerr coupling is the maximal.