A Study of the Efficiency of the Class of <Emphasis Type="Italic">W</Emphasis>-States as a Quantum Channel

Recently, a new class of W-states has been defined by Agarwal and Pati (Phys. Rev. A 74:062320, 2006) and it has been shown that they can be used as a quantum channel for teleportation and superdense coding. In this work, we identify those three-qubit states from the set of the new class of W-states which are most efficient or suitable for quantum teleportation. We show that with some probability is best suited for teleportation channel in the sense that it does not depend on the input state.     

Controlling on Entangled Decoherence by the Interaction Model Between Qubit and Environment

The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that the entanglement of quantum systems depends on not only the initial state of system but also the coupling ways between qubit and environment. It shows that: (1) when the system is initially in ( | 00 ?±| 11 ?)/?2( | 00 \rangle\pm| 11 \rangle)/\sqrt{2} state or in the mixed state which is produced by the state, if we can control the coupling between the qubits and the environment in a asymmetrical state, we can make the quantum system always in the entangled state. (2) For an initial state ( | 01 ?±| 10 ?)/?2( | 01 \rangle\pm| 10 \rangle)/\sqrt{2} or in its mixed state, in contrast, there will not be entangled death under the symmetric coupling. We also find that, in ( | 01 ?±| 10?)/?2( | 01 \rangle\pm| 10\rangle)/\sqrt{2} or in its mixed state, the stronger the interaction between qubits is, the better to struggle against entanglement sudden death is.     

Comparison and Analysis of the Control Power Between Two Different Perfect Controlled Teleportation Schemes Using Four-particle Cluster State

Control power is used to discuss about the controller’s measurable authority. It’s a new index to describe the controlled teleportation schemes from the point of view of the controller. In this paper, we introduce two perfect controlled teleportation schemes and calculate the control power under different control particles. In scheme 1, the controller just controls one particle, which is particle 2. And in scheme 2, the controller controls the particles 2 and 3. They both use the cluster state \(|\psi \rangle _{1234}=\frac {1}{2}(|0000\rangle +|0011\rangle +|1100\rangle -|1111\rangle )_{1234}\) as communication channel. By calculating the control power between two schemes, the control power of scheme 1 is 1/3, which is the minimal value of control power. On the contrary, the control power of scheme 2 is maximal, 1/2. Scheme 2 which controls two particles successfully promotes the control power comparing with scheme 1. It’s evidently that controlling particle 2 is a necessary condition. And controlling particle 3 can gain the control power but the controller cannot control it solely.     

Kraus Operator-Sum Representation and Time Evolution of Distribution Functions in Phase-Sensitive Reservoirs

Using the thermal entangled state representation 〈η|, we examine the master equation (ME) describing phase-sensitive reservoirs. We present the analytical expression of solution to the ME, i.e., the Kraus operator-sum representation of density operator ρ is given, and its normalization is also proved by using the IWOP technique. Further, by converting the characteristic function χ(λ) into an overlap between two “pure states” in enlarged Fock space, i.e., χ(λ)=〈η _=−λ |ρ|η ₌₀〉, we consider time evolution of distribution functions, such as Wigner, Q- and P-function. As applications, the photon-count distribution and the evolution of Wigner function of photon-added coherent state are examined in phase-sensitive reservoirs. It is shown that the Wigner function has a negative value when kt\leqslant\frac 12ln( 1+m_￥) \kappa t\leqslant\frac {1}{2}\ln ( 1+\mu_{\infty}) is satisfied, where μ _∞ depends on the squeezing parameter |M|² of environment, and increases as the increase of |M|.     

A Generalized Hadamard-Fresnel Complementary Transformation Derived by Virtue of New Coherent-Entangled State

The new coherent-entangled state |z,x;θ〉 is proposed in the two-mode Fock space, which exhibits both the properties of coherent and entangled states. The completeness relation of |z,x;θ〉 is proved by virtue of the technique of integral within an ordered product of operators. A generalized Hadamard-Fresnel complementary transformation derived by virtue of the coherent-entangled state |z,x;θ〉, which is unitary. The new unitary operator plays the role of both Hadamard transformation for ([^(a)]₁sinq-[^(a)]₂cosq)(\hat{a}_{1}\sin\theta -\hat{a}_{2}\cos\theta) and Fresnel transformation for ([^(a)]₁cosq+[^(a)]₂sinq)(\hat{a}_{1}\cos\theta +\hat{a}_{2}\sin\theta), respectively.     

The Controlled Teleportation of an Arbitrary Two-Atom Entangled State in Driven Cavity QED

In this paper, we propose a scheme for the controlled teleportation of an arbitrary two-atom entangled state |φ〉₁₂=a|gg〉₁₂+b|ge〉₁₂+c|eg〉₁₂+d|ee〉₁₂ in driven cavity QED. An arbitrary two-atom entangled state can be teleported perfectly with the help of the cooperation of the third side by constructing a three-atom GHZ entangled state as the controlled channel. This scheme does not involve apparent (or direct) Bell-state measurement and is insensitive to the cavity decay and the thermal field. The probability of the success in our scheme is 1.0.     

Relationship between capture coefficient and capture cross-section: Average velocity of a maxwellian distribution of carriers in a medium with an anisotropic effective mass tensor

The capture cross section of a trapping or recombination center for a charge carrier has been defined as the quotient of the capture coefficient and the average thermal velocity of the carrier distribution. For a Maxwellian distribution in a semiconductor band with an ellipsoidal effective mass tensor, this average velocity can be expressed as

Low Temperature Properties for Correlation Functions in Classical N-Vector Spin Models

We obtain convergent multi-scale expansions for the one-and two-point correlation functions of the low temperature lattice classical N - vector spin model in d S 3 dimensions, N S 2. The Gibbs factor is taken as exp[-b(1/2 ||?f||² +l/8 || |f|² - 1 ||² + v/2||f- h||²)], \exp [-\beta (1/2 ||\partial \phi||^2 +\lambda/8 ||\, |\phi|^2 - 1 ||^2 + v/2||\phi - h||^2)], where f(x), h ? R^N\phi(x), h \in R^N, x ? Z^dx \in Z^d, |h|=1, b < ￥|h|=1, \beta < \infty, l 3 ￥\lambda \geq \infty are large and 0 < v h 1. In the thermodynamic and v ˉ 0v \downarrow 0 limits, with h = e₁, and j L ‘^½ ‘, the expansion gives áf₁(x)? = 1+0(1/b^1/2)\langle \phi_1(x)\rangle = 1+0(1/\beta^{1/2}) (spontaneous magnetization), áf₁(x)f_i(y)? = 0\langle \phi_1(x)\phi_i(y)\rangle=0, áf_i (x)f_i (y)? = c₀ D^-1(x,y)+R(x,y)\langle \phi_i (x)\phi_i (y)\rangle = c_0 \Delta^{-1}(x,y)+R(x,y) (Goldstone Bosons), i = 2, 3, ?, Ni= 2, 3,\,\ldots, N, and áf₁(x)f₁(y)?^T=R￠(x,y)\langle \phi_1(x)\phi_1(y)\rangle^T=R'(x,y), where |R(x,y)||R(x,y)|, |R￠(x,y)| < 0(1)(1+|x-y|)^d-2+r|R'(x,y)|< 0(1)(1+|x-y|)^{d-2+\rho} for some „ > 0, and c₀ is aprecisely determined constant.     

Entangled Husimi Distribution and Complex Wavelet Transformation

Similar in spirit to the preceding work (Int. J. Theor. Phys. 48:1539, 2009) where the relationship between wavelet transformation and Husimi distribution function is revealed, we study this kind of relationship to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that, up to a Gaussian function, the entangled Husimi distribution function of a two-mode quantum state |ψ〉 is just the modulus square of the complex wavelet transform of e^-|h|2/2e^{-\vert \eta \vert ^{2}/2} with ψ(η) being the mother wavelet.     

Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

Virial Theorem for Angular Displacement and Torque

The usual Virial theorem is expressed through the coordinate and the force, 2áT? = áX\fracdVdX? = -áXF?2\langle T\rangle =\langle X\frac{dV}{dX}\rangle =-\langle XF\rangle , F=-\fracdVdXF=-\frac{dV}{dX}, XF is the work done by the force F, T is the kinetic energy. In this paper we extend the usual discussion on the Virial theorem about coordinate-force variables to the case of angular displacement-torque variables. By virtue of introducing the entangled state representation and the bosonic operator realization of the Hamiltonian of quantum pendulum system we derive the Virial theorem for angular variable and torque.     

The Transformations from the New Intermediate Entangled State

The new intermediate entangled state |η;θ〉 is proposed by virtue of IWOP technique, which is the common eigenvector of [([^(x)]₁ - [^(x)]₂)cosq-([^(p)]₁ - [^(p)]₂)sinq][(\hat{x}_{1} - \hat{x}_{2})\cos\theta -(\hat{p}_{1} - \hat{p}_{2})\sin\theta ] and [([^(x)]₁ +[^(x)]₂)sinq+ ([^(p)]₁ + [^(p)]₂)cosq][(\hat{x}_{1} +\hat{x}_{2})\sin\theta + (\hat{p}_{1} + \hat{p}_{2})\cos\theta ]. The squeezing transformation operator, Hadamard transformation operator, Fresnel transformation operator and Radon transform operator are constructed by |η;θ〉.     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

Stochastic Porous Media Equations and Self-Organized Criticality: Convergence to the Critical State in all Dimensions

If X = X(t, ξ) is the solution to the stochastic porous media equation in O ì R^d, 1 ￡ d ￡ 3,{\mathcal{O}\subset \mathbf{R}^d, 1\le d\le 3,} modelling the self-organized criticality (Barbu et al. in Commun Math Phys 285:901–923, 2009) and X _c is the critical state, then it is proved that ò^￥₀m(O\O^t₀)dt < ￥,\mathbbP-a.s.{\int^{\infty}_0m(\mathcal{O}{\setminus}\mathcal{O}^t_0)dt<{\infty},\mathbb{P}\hbox{-a.s.}} and lim_t?￥ ò_O|X(t)-X_c|dx = l < ￥, \mathbbP-a.s.{\lim_{t\to{\infty}} \int_\mathcal{O}|X(t)-X_c|d\xi=\ell<{\infty},\ \mathbb{P}\hbox{-a.s.}} Here, m is the Lebesgue measure and O^t_c{\mathcal{O}^t_c} is the critical region {x ? O; X(t,x)=X_c(x)}{\{\xi\in\mathcal{O}; X(t,\xi)=X_c(\xi)\}} and X _c (ξ) ≤ X(0, ξ) a.e. x ? O{\xi\in\mathcal{O}}. If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), lim_{t ? ￥} ò_K|X(t)-X_c|dx = 0{\lim_{t \to {\infty}} \int_K|X(t)-X_c|d\xi=0} exponentially fast for all compact K ì O{K\subset\mathcal{O}} with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case ℓ = 0.     

Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Condensation of the Roots of Real Random Polynomials on the Real Axis

We introduce a family of real random polynomials of degree n whose coefficients a _k are symmetric independent Gaussian variables with variance , indexed by a real α≥0. We compute exactly the mean number of real roots 〈N _n 〉 for large n. As α is varied, one finds three different phases. First, for 0≤α<1, one finds that . For 1<α<2, there is an intermediate phase where 〈N _n 〉 grows algebraically with a continuously varying exponent, . And finally for α>2, one finds a third phase where 〈N _n 〉∼n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots 〈N _n 〉/n are real. This condensation occurs via a localization of the real roots around the values , 1≪k≤n.     

Striped Periodic Minimizers of a Two-Dimensional Model for Martensitic Phase Transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Müller (Philos Mag A 66(5):697–715, 1992), is defined by the following functional:

Entanglement and Mixedness of Locally Cloned Non-Maximal W-State

In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W-state or W-type state |X〉=α|001〉₁₂₃+β|010〉₁₂₃+γ|100〉₁₂₃,α ²+β ²+γ ²=1 shared by three distant partners. Also we have considered the case β=γ, to obtain a range for α ², for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixedness of inseparable states with their amount of inseparability, for that range of α ².     

Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-Stage Tracking of Cosmological Nuclear Energy

Recent observations on Type-Ia supernovae and low density (Ω _m =0.3) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity type ‘exotic matter’ with negative-pressure often said ‘dark energy’ (Ω _x =0.7). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to reveal the genesis of dark energy and suggest that ‘the cosmological nuclear binding energy liberated during primordial nucleo-synthesis remains trapped for a long time and then is released free which manifests itself as dark energy in the universe’. It is also explained why for dark energy the parameter w=-\frac23w=-\frac{2}{3} . Noting that w=1 for stiff matter and w=\frac13w=\frac{1}{3} for radiation; w=-\frac23w=-\frac{2}{3} is for dark energy because “−1” is due to ‘deficiency of stiff-nuclear-matter’ and that this binding energy is ultimately released as ‘radiation’ contributing “ +\frac13+\frac{1}{3} ”, making w=-1+\frac13=-\frac23w=-1+\frac{1}{3}=-\frac{2}{3} . When dark energy is released free at Z=80, w=-\frac23w=-\frac{2}{3} . But as on present day at Z=0 when the radiation-strength-fraction (δ), has diminished to δ→0, the w=-1+d\frac13=-1w=-1+\delta\frac{1}{3}=-1 . This, almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several estimates/predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a possible candidate for dark energy.     

Dissipative Future Universe Without Big Rip

The present study deals with dissipative future universe without big rip in context of Eckart formalism. The generalised Chaplygin gas, characterised by equation of state p=-\fracAr^\frac1ap=-\frac{A}{\rho^{\frac{1}{\alpha}}}, has been considered as a model for dark energy due to its dark-energy-like evolution at late time. It is demonstrated that, if the cosmic dark energy behaves like a fluid with equation of state p=ωρ; ω<−1 as well as Chaplygin gas simultaneously then the big rip problem does not arise and the scale factor is found to be regular for all time.