Sharing of classical and quantum correlations via XY interaction

The sharing of classical and quantum correlations via XY interaction is investigated. The model includes two identical networks consisting of n$n$ nodes, the i$i$th node of one network sharing a correlated state with the j$j$th node of the other network, while all other nodes are initially unconnected. It is shown that classical correlation, quantum discord as well as entanglement can be shared between any two nodes of the network via XY interaction and that quantum information can be transferred effectively between them. It is found that there is no simple dominating relation between the quantum correlation and entanglement in inertial system.     

Entanglement entropy and variational methods: Interacting scalar fields

We develop a variational approximation to the entanglement entropy for scalar ?⁴${?}^4$ theory in 1+1$1+1$, 2+1$2+1$, and 3+1$3+1$ dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+1$1+1$ and 2+1$2+1$ dimensions, the entanglement entropy of ?⁴${?}^4$ theory as a function of coupling is monotonically decreasing and convex. While ?⁴${?}^4$ theory with positive bare coupling in 3+1$3+1$ dimensions is thought to lead to a trivial free theory, we analyze a version of ?⁴${?}^4$ with infinitesimal negative bare coupling, an asymptotically free theory known as precarious  ?⁴${?}^4$ theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious ?⁴${?}^4$ theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling.     

Probing Planckian physics in de Sitter space with quantum correlations

We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular α$\alpha$-vacuum has been considered. We show the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch–Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quantum gravitational effects via quantum information methodology in future. Beyond single-mode approximation, we construct proper Unruh modes admitting general α$\alpha$-vacua, and find a convergent feature of both bosonic and fermionic entanglements. In particular, we show that the convergent points of fermionic entanglement negativity are dependent on the choice of α$\alpha$. Moreover, an one-to-one correspondence between convergent points H_c$H_c$ of negativity and zeros of quantum capacity of quantum channels in de Sitter space has been proved.     

Two charges on a plane in a magnetic field: II. Moving neutral quantum system across a magnetic field

The moving neutral system of two Coulomb charges on a plane subject to a constant magnetic field B$B$ perpendicular to the plane is considered. It is shown that the composite system of finite total mass is bound for any center-of-mass momentum P$P$ and magnetic field strength; the energy of the ground state is calculated accurately using a variational approach. Its accuracy is cross-checked in a Lagrange-mesh method for B=1$B=1$  a.u. and in a perturbation theory at small B$B$ and P$P$. The constructed trial function has the property of being a uniform approximation of the exact eigenfunction. For a Hydrogen atom and a Positronium a double perturbation theory in B$B$ and P$P$ is developed and the first corrections are found algebraically. A phenomenon of a sharp change of energy behavior for a certain center-of-mass momentum and a fixed magnetic field is indicated.     

Cyclic groups and quantum logic gates

We present a formula for an infinite number of universal quantum logic gates, which are 4$4$ by 4$4$ unitary solutions to the Yang–Baxter (Y–B) equation. We obtain this family from a certain representation of the cyclic group of order n$n$. We then show that this discrete   family, parametrized by integers n$n$, is in fact, a small sub-class of a larger continuous   family, parametrized by real numbers θ$\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.     

Generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy

We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order q$q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for q=2$q=2$ or 3$3$. This generalization encapsulates the multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-q$q$ entropy for 1≤q≤2$1\le q\le 2$ or 3≤q≤4$3\le q\le 4$, which also contains the multi-qubit polygamy inequality as a special case.     

A study on the relations between the topological parameter and entanglement

In this Letter, some relations between the topological parameter d   and concurrences of the projective entangled states have been presented. It is shown that for the case with d=n$d=n$, all the projective entangled states of two n  -dimensional quantum systems are the maximally entangled states (i.e. C=1$C=1$). And for another case with d≠n$d\ne n$, C   both approach 0 when d→+∞$d\to +\infty$ for n=2$n=2$ and 3. Then we study the thermal entanglement and the entanglement sudden death (ESD) for a kind of Yang–Baxter Hamiltonian. It is found that the parameter d   influences not only the critical temperature _Tc$T_c$ but also the maximum entanglement value that the system can arrive at. And we also find that the parameter d has a great influence on the ESD.     

Improved quantum state transfer via quantum partially collapsing measurements

In this work, we present a general scheme to improve quantum state transfer (QST) by taking advantage of quantum partially collapsing measurements. The scheme consists of a weak measurement performed at the initial time on the qubit encoding the state of concern and a subsequent quantum reversal measurement at a desired time on the destined qubit. We determine the strength q_r$q_r$ of the post quantum reversal measurement as a function of the strength p$p$ of the prior weak measurement and the evolution time t$t$ so that near-perfect QST can be achieved by choosing p$p$ close enough to 1, with a finite success probability, regardless of the evolution time and the distance over which the QST takes place. The merit of our scheme is twofold: it not only improves QST, but also suppresses the energy dissipation, if any.     

Third-harmonic generation in asymmetric coupled quantum wells

The third-harmonic generation (THG) in asymmetric coupled quantum wells (ACQWs) for different values of the well parameter Δ$\Delta$ and width of barrier (_WB)$\left(W_B\right)$ are theoretically studied. The analytical expression of the third-harmonic generation is derived by using the compact density-matrix approach and the iterative method. Finally, the numerical calculations are presented for typical GaAs/Al_xGa_1−xAs asymmetric coupled quantum wells. Results obtained show that the third-harmonic generation in the asymmetric coupled quantum wells can be importantly modified by the parameter Δ$\Delta$ and _WB$W_B$. Moreover, third-harmonic generation also depends on the relaxation rate of the asymmetric coupled quantum wells.     

Deterministic LOCC transformation of three-qubit pure states and entanglement transfer

A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a partially ordered set parametrized by five well-known entanglement parameters and a novel parameter; the five are the concurrences C_AB$C_{AB}$, C_AC$C_{AC}$, C_BC$C_{BC}$, the tangle τ_ABC${\tau }_{ABC}$ and the fifth parameter J₅$J_5$ of Acín et al. (2000) Ref. [19], while the other new one is the entanglement charge Q_e$Q_{\text{e}}$. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen’s work (Nielsen (1999) [14]) to three-qubit pure states. We also clarify the rules of transfer and dissipation of the entanglement which is caused by deterministic LOCC transformations. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation between three-qubit pure states is given.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

We have studied the stochastic resonance (SR) of bistable systems coupled to a bath with a nonlinear system–bath interaction, by using the microscopic, generalized Caldeira–Leggett (CL) model. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent (multiplicative) diffusion which preserve the fluctuation–dissipation relation (FDR). Results of our simulations are given as follows: (1) the spectral power amplification (SPA) exhibits SR not only for a$a$ and b$b$ but also for τ$\tau$ while the stationary probability distribution function is independent of them where a$a$ and b$b$ denote magnitudes of multiplicative and additive noises, respectively, and τ$\tau$ expresses the relaxation time of Ornstein–Uhlenbeck (OU) colored noise; (2) the SPA for coexisting additive and multiplicative noises has a single-peak but two-peak structure as functions of a$a$, b$b$ and/or τ$\tau$. Results (1) and (2) are qualitatively different from previous ones obtained by phenomenological Langevin models where the FDR is not held or indefinite. These show an importance of the FDR in a study on SR of open bistable systems.     

Graphite C-axis thermal conductivity

This paper models the c$c$-axis thermal conductivity of thin graphite layers taking into account phonon confinement. A Debye model is used to calculate graphite c$c$-axis thermal conductivity, which is found to be 4 orders of magnitude smaller than in the graphite basal plane. This reduced thermal conductivity is promising for devices with improved thermoelectric figure of merit, ZT$ZT$, and thermal conduction along graphite c$c$-axis. Results of graphite thermal conductivity in the basal plane are also presented and discussed. These calculations have been done for ideal graphite structures that are a few monolayers thick, free of defects, and free of boundary scattering processes. To achieve the low calculated values of thermal conductivity, it will be necessary to fabricate high-quality graphite structures; this will pose significant fabrication challenges.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

The dynamics of quantum correlation with two controlled qubits under classical dephasing environment

We discuss the quantum correlation dynamics of two qubits controlled through the application of π$\pi$-pulses under classical dephasing non-Markovian environment. It is shown that the quantum discord (QD) and one-norm geometric quantum discord (one-norm GQD) between the two qubits, which are prepared initially in the three-parameter-X$X$-type quantum states, depend strongly on non-Markovian properties and the time difference between adjacent pulses. The freezing time of discord and one-norm GQD can be lengthened for appropriate pulse separate time and pulse numbers. And the freezing time of one-norm GQD is longer slightly than QD for both Markovian and non-Markovian cases. What is more, we find that double sudden changes of one-norm GQD can appear only for some initial parameters when π$\pi$-pulses are applied.     

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0$T>0$ transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0$T=0$ 1D insulator the charge stiffness D(T)$D\left(T\right)$ vanishes for T>0$T>0$ and finite values of the on-site repulsion U$U$ in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T$T$ and U>0$U>0$ it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0$U=0$ and vanishes for U>0$U>0$ is found to result from a general transition from a conductor to an insulator or resistor occurring at U=U_c=0$U=U_c=0$ for all finite temperatures T>0$T>0$. (At T=0$T=0$ such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η$\eta$-spin SU(2)$SU\left(2\right)$ symmetry with the hidden U(1)$U\left(1\right)$ symmetry beyond SO(4)$SO\left(4\right)$ is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.