Tighter Constraints of Multiqubit Entanglement

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement, and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.     

Monogamy and polygamy relations of multiqubit entanglement based on unified entropy

Monogamy relation is one of the essential properties of quantum entanglement,which characterizes the distribution of entanglement in a multipartite system.By virtual of the unified-(q,s) entropy,we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures.For the multiqubit system,a class of tighter monogamy relations are established in term of the a-th power of unified-(q,s) entanglement for a 1.We also obtain a class of tighter polygamy relations in the β-th(0≤β≤1) power of unified-(q,s) entanglement of assistance.Applying these results to specific quantum correlations,e.g.,entanglement of formation,Renyi-q entanglement of assistance,and Tsallisq entanglement of assistance,we obtain the corresponding monogamy and polygamy relations.Typical examples are presented for illustration.Furthermore,the complementary monogamy and polygamy relations are investigated for theα-th(0≤α≤1) and β-th(β≥1) powers of unified entropy,respectively,and the corresponding monogamy and polygamy inequalities are obtained.     

Complementary monogamy and polygamy properties among multipartite systems

Monogamy and polygamy relations are essential properties of quantum entanglement, which characterize the distributions of entanglement in multipartite systems. In this paper, we establish the general monogamy relations for γ-th(0 ≤ γ ≤ α, α ≥ 1) power of quantum entanglement based on unified-(q, s) entanglement and polygamy relations for δ-th(δ ≥ β, 0 ≤ β ≤ 1) power of entanglement of assistance based on unified-(q, s) entanglement of assistance, which provides a complement to the previous resea...     

Entanglement evolution of three-qubit mixed states in multipartite cavity—reservoir systems

We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state.For a composite system consisting of three cavities interacting with independent reservoirs,it is shown that the entanglement evolution is restricted by a set of monogamy relations.Furthermore,as quantified by the negativity,the entanglement dynamical property of the mixed entangled state of cavity photons is investigated.It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death(ESD).However,compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement,the ESD time of mixed states is later than that of the pure state.Finally,we discuss the entanglement distribution in the multipartite system,and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.     

Total versus quantum correlations in a two-mode Gaussian state

In Li and Luo(2007 Phys. Rev. A 76 032327), the inequality(1/2)T≥ Q was identified as a fundamental postulate for a consistent theory of quantum versus classical correlations for arbitrary measures of total T and quantum Q correlations in bipartite quantum states. Besides, Hayden et al(2006 Commun. Math. Phys. 265 95) have conjectured that, in some conditions within systems endowed with infinite-dimensional Hilbert spaces, quantum correlations may dominate not only half of total correlations but total correlations itself. Here, in a two-mode Gaussian state,quantifying T and Q respectively by the quantum mutual information I~G and the entanglement of formation(EoF) ε_F~G, we verify that ε_(F,R)~G,is always less than(1/2) I_R~G when I~G and ε_F~G are defined via the Rényi-2 entropy. While via the von Neumann entropy, ε_(F,V)~G,may even dominate I_V~G itself,which partly consolidates the Hayden conjecture, and partly, provides strong evidence hinting that the origin of this counterintuitive behavior should intrinsically be related to the von Neumann entropy by which the EoF ε_(F,V)~G,is defined, rather than related to the conceptual definition of the EoF ε_F. The obtained results show that—in the special case of mixed two-mode Gaussian states—quantum entanglement can be faithfully quantified by the Gaussian Rényi-2 EoF ε_(F,R)~G,.     

Monogamy of quantum correlations in the one-dimensional anisotropic XY model

In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with stag- gered Dzyaloshinskii-Moriya （DM） interaction have been investigated using the quantum renormalization group （QRG） method. We summarize the monogamy relation for different quantum correlation measures and make an explicit compar- ison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.     

Monogamy of quantum correlations in the one-dimensional anisotropic XXXYYY model

In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii–Moriya(DM) interaction have been investigated using the quantum renormalization group(QRG) method. We summarize the monogamy relation for different quantum correlation measures and make an explicit comparison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.     

Monogamy relations in tripartite quantum system

This paper presents monogamy relations for three-qubit quantum states by using convex-roof extended negativity, which inspires studying the difference between the three entanglement measures, concurrence, negativity and convexroof extended negativity. It finds that the convex-roof extended negativity is a stronger entanglement measure than concurrence in multipartite higher-dimensional quantum system.     

Entanglement Capabilities of Non-local Hamiltonians with Maximally Entangled Ancillary Particles

The entanglement capacity of non-local two-qubit Hamiltonians with maximally entangled ancillary particles are investigated.We gain a complete expression of entanglement capacity and show that the maximal entanglement capacity Γmax of a non-local Hamiltonian with ancillary particles will be never less than the maximal entanglement capacity Γ*max of the non-local Hamiltonian without ancillary particles.By defining relative entanglement rate η=Γmax /Γ*max (Γmax, Γ*max are maximal entanglement rate with and without ancillas respectively), we find the range of the values of relative entanglement rate is 1η1.3220.     

Effects of dipole-dipole interaction on entanglement transfer

A system consisting of two different atoms interacting with a two-mode vacuum, where each atom is resonant only with one cavity mode, is considered. The effects of dipole-dipole （dd） interaction between two atoms on the atom-atom entanglement and mode--mode entanglement are investigated. For a weak dd interaction, when the atoms are initially separable, the entanglement between them can be induced by the dd interaction, and the entanglement transfer between the atoms and the modes occurs efficiently; when the atoms are initially entangled, the entanglement transfer is almost not influenced by the dd interaction. However, for a strong dd interaction, it is difficult to transfer the entanglement from the atoms to the modes, but the atom-atom entanglement can be maintained when the atoms are initially entangled.     

Scaling of entanglement entropy for spin chain with Dzyaloshinskii-Moriya interaction

This paper investigates the entanglement in an XX-type spin chain with Dzyaloshinskii-Moriya interaction under an external magnetic field.The von Neumann entropy of entanglement between two blocks for the ground state of the system is evaluated.It analyses and discusses the scaling behaviour of the entanglement entropy.     

Relative entropy of entanglement of two-qubit ’X’ states

Two closest single-qubit states could be diagonalised by the same unitary matrix,which helps to find the relative entropy of entanglement of a two-qubit ’X’ state.We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ’X’ state.This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states,such as pure states,Werner states,and so on.     

Effect of mode mode-competition on atom-atom entanglement

A system consisting of two atoms interacting with a two-mode vacuum is considered, where each atom is resonant with the two cavity modes through two different competing transitions. The effect of mode--mode competition on the atom--atom entanglement is investigated. We find that the entanglement between the two atoms can be induced by the mode--mode competition. For the initial atomic state |\varPsi(0)\rangle, whether the atoms are initially separated or entangled, a large or even maximal entanglement between them can be obtained periodically by introducing the mode--mode competition. For the initial atomic state |\varPhi(0)\rangle, the strong mode--mode competition can prevent the two atoms entangled initially from suffering entanglement sudden death; besides, it makes them in a more stable and longer-lived entanglement than in the non-competition case.     

A 9 × 9 matrix representation of Temperley-Lieb algebra and corresponding entanglement

We present the matrix U.The 9×9 U matrix is a representation of specialized Temperley-Lieb algebra.Based on which,a unitary R matrix is generated via the Yang-Baxterization approach.The 9×9 R matrix,a solution of the Yang-Baxter equation,is universal for quantum entanglement.     

Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain

We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J1 > J for J > 0, and J1 > 0 for J < 0, and in these two regions C increases with the increase of J1, so is the critical temperature Tc. When J1 >>|J| , C reaches its maximum value 0.5 and Tc reaches the asymptotic value Tc = 3.41448J1. For entanglement between the normal lattices, C appears only when J > 0 and 2J < J1 < J, and initially increases with the increase of J1 and arrives at the maximum value Cmax = (e4JIT-3)/(e4JIT+3) before it decays to zero gradually, so is the critical temperature Tc with, however, the maximum value Tcmax = 4J/ln3.     

Dynamics of vibrational chaos and entanglement in triatomic molecules： Lie algebraic model

In this paper, the dynamics of chaos and the entanglement in triatomic molecular vibrations are investigated. On the classical aspect, we study the chaotic trajectories in the phase space. We employ the linear entropy to examine the dynamical entanglement of the two bonds on the quantum aspect. The correspondence between the classical chaos and the quantum dynamical entanglement is also investigated. As an example, we apply our algebraic model to molecule H2O.     

Multi-impurity effects on the entanglement of anisotropic Heisenberg ring XXZ under a homogeneous magnetic field

The effects of multi-impurity on the entanglement of anisotropic Heisenberg ring XXZ under a homogeneous magnetic field are studied. The impurities make the equal pairwise entanglement in a ring compete with each other so that the pairwise entanglement exhibits oscillation. If the impurities are of larger couplings, both the critical temperature and pairwise entanglement can be improved.     

Dynamical control of population and entanglement for open Λ-type atoms by engineering the environment

The exactly analytical solution for the dynamics of the dissipative Λ-type atom in the zero-temperature Lorentzian environment is presented. On this basis, we study the evolution of the population and entanglement. We find that the stable populations on the two lower levels of the Λ-type atom can be effectively adjusted by the combination of the relative decay rate and the environmental spectral frequency. However, for the initial Werner-like state, the stable entanglement between the two Λ-type atoms has very little tunability. Furthermore, the stable entanglement for the bilateral environment case is larger than that of the unilateral environmental case. A nonintuitive relation between the stable entanglement and stable population is found.     

Quantum entanglement in the system of a moving V-type three-level atom interacting with the SU（1,1）-related coherent fields

In a system with a moving V-type three-level atom interacting with the SU(1,1)-related coherent fields, we investigate the entanglement between the moving three-level atom and the SU(1,1)-related coherent fields by using the quantum-reduced entropy, and that between the SU(1,1)-related coherent fields by using the quantum relative entropy of entanglement. It is shown that the two kinds of entanglement are dependent on the atomic motion and exhibit the periodic evolution with a period of 2π/p. The maximal atom--field qutrit entanglement state can be prepared, and the entanglement preservation of the SU(1,1)-related coherent fields can be realized in the interacting process via the appropriate selection of system parameters and interaction time.     

Quantum Coherence Quantifiers Based on Rényi α-Relative Entropy

The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity property for the coherence measures induced by the Rényi α-relative entropy, which present in [Phys. Rev. A 94(2016) 052336]. We show that the Rényi α-relative entropy of coherence does not in general satisfy the monotonicity requirement under the subselection of measurements condition and it also does not satisfy the extension of monotonicity requirement, which presents in [Phys.Rev. A 93(2016) 032136]. Due to the Rényi α-relative entropy of coherence can act as a coherence monotone quantifier,we examine the trade-off relations between coherence and mixedness. Finally, some properties for the single qubit of Rényi 2-relative entropy of coherence are derived.