Quantum Discord Behaviors in Two Qubits Spin Squeezing Model with Intrinsic Decoherence

By taking into account the intrinsic decoherence and the external magnetic field, quantum discord(QD) behaviors in two-qubit spin squeezing model are investigated in detail. It is found that the magnitude of quantum discord is strongly dependent on the initial states, the squeezing interaction μ, the magnetic field Ω and the purity r of initial states. With t → ∞, one can obtain the steady quantum discord (SQD) value, the environmental decoherence cannot entirely destroy the quantum correlation. Based on the analysis of the SQD, the conditions about the existence of SQD are obtained with different initial states. Varying the parameters μ, Ω and r not only can weaken the effects of decoherence but also can improve the magnitude of QD and SQD. The effects of the parameters μ and Ω on the QD and SQD display so different and complicated features that one cannot get an uniform law about them, while the values of QD and SQD are improved with increasing r. Properly tuning the parameters μ, Ω and r, one can obtain a larger value of QD or SQD.     

Quantum Dense Coding About a Two-Qubit Heisenberg XYZ Model

By taking into account the nonuniform magnetic field, the quantum dense coding with thermal entangled states of a two-qubit anisotropic Heisenberg XYZ chain are investigated in detail. We mainly show the different properties about the dense coding capacity (χ) with the changes of different parameters. It is found that dense coding capacity χ can be enhanced by decreasing the magnetic field B, the degree of inhomogeneity b and temperature T, or increasing the coupling constant along z-axis J _z . In addition, we also find χ remains the stable value as the change of the anisotropy of the XY plane Δ in a certain temperature condition. Through studying different parameters effect on χ, it presents that we can properly turn the values of B, b, J _z , Δ or adjust the temperature T to obtain a valid dense coding capacity (χ satisfies χ > 1). Moreover, the temperature plays a key role in adjusting the value of dense coding capacity χ. The valid dense coding capacity could be always obtained in the lower temperature-limit case.     

Thermal Entanglement Properties in two Kinds of Two-qubit Spin Squeezing Model

Using the concurrence (C) criterion, we investigate the thermal entanglement properties in two-qubit spin squeezing model for two kinds of squeezing interaction: one-axis twisting model (OATM) and two-axis countertwisting model (TACM) with a transverse field. To the OATM, in the limit case of T→0, the ground state entanglement is initially increased from zero to the maximum value, then decreased in a period of time and suddenly disappeared finally with further enhancing the external magnetic field Ω. One interesting thing is that instead of decaying slowly to zero the entanglement is sudden disappeared with further enhancing Ω or μ (the spin squeezing interaction in X direction), and decreasing the parameter μ or Ω can obviously broaden the scope of entanglement exists. For the finite temperature case, a novelty point is the sudden birth phenomenon occured in the behaviors of entanglement, it is initially to be zero (persists for some time), with further improving Ω and μ the entanglement will be suddenly appeared, and the time interval (persists to be zero) before sudden birth is obviously prolonged with decreasing two parameters. The temperature range of entanglement exists can be extended evidently with increasing μ or Ω, and one can obtain entanglement at higher temperature through changing them. When to the TACM, the ground state entanglement is initially decreased from the maximum value and then suddenly disappeared with increasing Ω. While increasing γ the ground state entanglement is increased initially from zero to the maximum value and then sudden disappeared with further improving γ (the spin squeezing interaction in XY plane), proper tuing γ or Ω can prolong the lives of entanglement evidently. For the finite temperature case, the sudden birth phenomenon also occured in the the evoluted concurrence, the variation of parameters Ω and γ can reduce the time interval before sudden birth. The influence of the temperature T on thermal entanglement property is also investigated. The temperature range of entanglement existence can be extended evidently with increasing γ, one can obtain entanglement at higher temperature through changing parameters γ and Ω.     

Generation and Preparation of the Sustained Optimal Entropy Squeezing State of a Motional Atom Inside Vacuum Cavity

Considering two two-level atoms initially in Bell state, we send one atom into a vacuum cavity while leaving the other outside, and consider the motion of atom inside the cavity. Using quantum information entropy squeezing theory, the time evolution of the entropy squeezing factor of atom inside the cavity is discussed for two cases, i.e., before and after performing rotation operations and measuring atom outside, the influences of the field mode structure and atomic motions on the atomic entropy squeezing are evaluated. It is shown that atom inside the cavity has no entropy squeezing phenomenon before operating atom outside the cavity. However, the optimal entropy squeezing phenomenon of period T = 2π/p emerges and constant entropy squeezing phenomenon can occur by adjusting rotation operation to R(π/4), and setting the field mode structure parameter 0 < p < 50. In particular, if choosing p > 50, a sustained optimal entropy squeezing state (SOESS) can be generated. We also present the schematic circuit diagram of preparation of SOESS. Our proposal provides a possible way for the initial decoherent state recovering into sustained maximal coherent superposition state of single atom in the quantum noise environment.     

Pure and mixed states in degenerate parametric oscillation

The degree of purity of the quantum state of electromagnetic field at the output of a degenerate optical parametric oscillator is theoretically analyzed. It is shown that, in the subthreshold and significantly suprathreshold modes, the degree of purity of the state of pairs of waves with frequencies ω _s ± Ω (ω _s is the signal mode frequency) is unity. Based on this fact, it is concluded that these pairs of waves parametrically develop independent of any other such pairs. At the same time, in the suprathreshold mode near the oscillation threshold, the degree of purity of wave pairs can be much smaller than unity. However, consideration of a tetrad of waves with frequencies ω _s ± Ω and ω _p ± Ω shows that this system is in a pure state, which indicates its independent development.     

The New Multipartite Squeezing Operator and Some of its Properties

In this paper, we introduce a pair of mutually conjugate multipartite entangled state representations for defining the squeezing operator of entangled multipartite S_n(λ) which involves an n-mode bosonic operator realization of the SU(1,1) Lie algebra. This operator squeezes the multipartite entangled state in a natural way. We discuss the transform properties of a_j and \(a_{j}^{\dagger }\) under the operation of S_n(λ) and derive the interaction Hamiltonian which can generate such an evolution. In addition, the corresponding multipartite squeezed vacuum state |λ〉 is obtained. Based on this, the variances of the n-mode quadratures in |λ〉 are evaluated and the violation of the Bell inequality for |λ〉 is examined by using the formalism of Wigner representation.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Teleportation of aTripartite Squeezed Entangled State Via EPR Entangled State with Continuous Variables

A scheme for teleporting an arbitrary tripartite entangled state is proposed when three bipartite entangled states (|η〉) with continuous variables are used as quantum channels. Quantum teleportation can be carried out successfully if the receiver adopts an appropriate unitary transformation. The calculation is greatly simplified by virtue of the Schmidt decompositions of both tripartite entangled state |p _t ,χ ₂,χ ₃〉 and |η〉. Any tripartite state which can be expanded in terms of |p _t ,χ ₂,χ ₃〉 may be teleported in this way due to the completeness of |p _t ,χ ₂,χ ₃〉.     

Various Quantum Correlations in Two-Qubit Two-Axis Spin Squeezing Model in Thermal Equilibrium under an External Magnetic Field

This paper investigates the influence of the spin squeezing parameter γ, the external magnetic field B and the temperature T on the concurrence (C), the quantum discord (QD), and the geometric quantum discord (GQD) in the two-qubit two-axis spin squeezing model in thermal equilibrium under an external magnetic field. The results show that the spin squeezing parameter γ has a positive effect on all three correlations. When the system is in the ground state, the external magnetic field B has a weakening effect on the three types of quantum correlations. Particularly, the spin squeezing parameter can be used to alleviate the destructive effect of the magnetic field on the geometric quantum discord. At a relatively high temperature, the externally applied magnetic field B helps enhance the quantum discord (QD). Further, the quantum discord is more robust than concurrence, and thus is more suitable for use as a quantum resource in information processing.     

A Liouville-type Theorem for Schrödinger Operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P ₁, such that a nonzero subsolution of a symmetric nonnegative operator P ₀ is a ground state. Particularly, if P _j : = ?Δ + V _j , for j = 0,1, are two nonnegative Schrödinger operators defined on \(\Omega\subseteq \mathbb{R}^d\) such that P ₁ is critical in Ω with a ground state φ, the function \(\psi\nleq 0\) is a subsolution of the equation P ₀ u = 0 in Ω and satisfies \(\psi_+\leq C\varphi\) in Ω, then P ₀ is critical in Ω and \(\psi\) is its ground state. In particular, \(\psi\) is (up to a multiplicative constant) the unique positive supersolution of the equation P ₀ u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds.     

An Alternative Model of the Damped Harmonic Oscillator Under the Influence of External Force

In this paper we introduce the modified time-dependent damped harmonic oscillator. An exact solution of the wave function for both Schrödinger picture and coherent state representation are given. The linear and quadratic invariants are also discussed and the corresponding eigenvalues and eigenfunctions are calculated. The Hamiltonian is transformed to SU(1,1) Lie algebra and an application to the generalized coherent state is discussed. It has been shown that when the system is under critical damping case the maximum squeezing is observed in the first quadrature F _x . However, for the overcritical damping case the maximum squeezing occurs in the second quadrature F _y . Also it has been shown that the system for both cases is sensitive to the variation in the coherent state phase.     

Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [?y(1 + β), x(1 ? β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| < 1 and hyperbolas for |β| > 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.     

Interplay of Curie-type and Pauli-type magnetic susceptibilities in HCl-doped polyaniline pellets

The static magnetic susceptibility (χ) of own-made HCl-doped polyaniline pellets is investigated experimentally over the full range of the protonation level Y and in the temperature (T) range 10–300 K.The obtained results suggest that χ and the electrical conductivity σ – which is known from previous work – are interrelated.Namely, there is a weakly Y dependent crossover temperature T ^* where both χ and σ undergo notable changes.In χ, this refers to a simultaneous enhancement (reduction) of the Pauli-type susceptibility χ _P and reduction (enhancement) of the Curie constant C at T = T ^* when T increases (decreases).Below T < T ^*, where thermal effects are weak to moderate, a steep increase of χ _P(Y) around Y = 0.3 occurs together with a drop of C(Y).The above findings are consistent with a picture in which, at T ^*, spins that disappear from C reappear in χ _P, and vice versa.This model is used to address the longitudinal and transversal electron localisation lengths as functions of Y, the former being estimated to take values in the range 7–8 Åand the latter in the range 1–2 Å.     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

The Quantum Dense Coding in a Two Atomic System Under the Non-Markovian Environment

The quantum dense coding in a two atomic system under the non-Markovian environment is investigated in detail. We mainly concentrate on the effects about the environment parameter Γ(or γ) and the purity r of the initial state on the dense coding capacity χ. It is found that the dense coding capacity χ is initially decreased and gradually trends to be a constant nonzero value with evolution of time for different environment parameter Γ(or γ). This constant value is determined the initial state and independent to the environment. In other word, environment noise only affects the process of quantum dense coding, but not affects the final result of dense coding capacity. The purity r of the initial state has a strong influence on the initial value of the χ. Besides, for one value r, dense coding capacity χ is decreased firstly, and then reaches a stable value for a long time, whatever the values of other parameters are, but when the purity r of the initial state increased, the initial value of dense coding capacity increased.

     

Entanglement measure for pure <Emphasis Type="Italic">M</Emphasis> ⊗ <Emphasis Type="Italic">N</Emphasis> bipartite quantum states

We propose an entanglement measure for pure M ? N bipartite quantum states. We obtain the measure by generalizing the equivalent measure for a 2 ? 2 system, via a 2 ? 3 system, to the general bipartite case. The measure emphasizes the role Bell states have, both for forming the measure and for experimentally measuring the entanglement. The form of the measure is similar to the generalized concurrence. In the case of 2 ? 3 systems, we prove that our measure, which is directly measurable, equals the concurrence. It is also shown that, in order to measure the entanglement, it is sufficient to measure the projections of the state onto a maximum of M(M ? 1)N(N ? 1)/2 Bell states.     

Entangled Two Two-Level Atom in the Presence of External Classical Fields

In this contribution, we investigate a TTLAs (two two-level atoms) in interaction with an electromagnetic field in presence of the external classical fields. The general solution of the time evolution operator is obtained and used to derive the density matrix operator. The temporal evolution of the atomic inversion, the degree of entanglement measured by the negativity, as well as the single atom entropy squeezing are discussed. We consider the atomic system at either the upper or Bell states, while the field in the coherent state. It has been shown that the coupling parameter g (the coupling of the external classical fields) gets more effective for the case in which the g is not equal to zero. Also for a strong coupling parameter g the superstructure phenomenon can be reported. The results shown that for increase the value of the classical external fields parameter leads to the entanglement between the atoms and the fields gets stronger. Also it has shown that for specific value of the classical external fields the system never reaches the pure state except during the revival periods.     

Bell(<Emphasis Type="Italic">δ</Emphasis>) Inequalities Derived from Separate Common Causal Explanation of Almost Perfect EPR Anticorrelations

It is a well known fact that a common common causal explanation of the EPR scenario which consists in providing a local, non-conspiratorial common common cause system for a set of EPR correlations is excluded by various Bell inequalities. But what if we replace the assumption of a common common cause system by the requirement that each correlation of the set has a local, non-conspiratorial separate common cause system? In the paper we show that this move does not yield a solution by providing a general recipe how to derive any Bell(δ) inequality—that is an inequality differing from some Bell inequality in a term of order of δ—from the assumption that an appropriate set of almost perfect anticorrelations has a separate common causal explanation.     

Large Violation of Bell Inequalities with Low Entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order \({\frac{\sqrt{n}}{\log n}}\) with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.     

Quantum Statistical Properties of the Codirectional Kerr Nonlinear Coupler in Terms of su$\left (\right ) $ Lie Group in Interaction with a Two-level Atom

The problem of the codirectional Kerr coupler has been considered several times from different point of view. In the present paper we introduce the interaction between a two-level atom and the codirectional Kerr nonlinear coupler in terms of su\(\left (2\right ) \) Lie algebra. Under certain conditions we have adjusted the Kerr coupler and consequently we have managed to handle the problem. The wave function is obtained by using the evolution operator where the Heisnberg equation of motion is invoked to get the constants of the motion. We note that the Kerr parameter χ as well as the quantum number j plays the role of controlling the atomic inversion behavior. Also the maximum entanglement occurs after a short period of time when χ = 0. On the other hand for the entropy and the variance squeezing we observe that there is exchange between the quadrature variances. Furthermore, the variation in the quantum number j as well as in the parameter χ leads to increase or decrease in the number of fluctuations. Finally we examined the second order correlation function where classical and nonclassical phenomena are observed.