SU(1,1) Coherent States for the Generalized Two-Mode Time-Dependent Quadratic Hamiltonian System

The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schrödinger cat states defined as an eigenstate of $\hat{K}_{-}^{2}The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schr?dinger cat states defined as an eigenstate of are also studied. We applied our development to two-mode Caldirola-Kanai oscillator which is a typical example of the time-dependent quadratic Hamiltonian system. The time evolution of the quadrature distribution for the probability density in the coherent states are analyzed for the two-mode Caldirola-Kanai oscillator by plotting relevant figures.     

Fidelity for States of Two Spin- $\frac{1}{2}$ Particles in Moving Frames

Fidelity for the spin part of states of two spin- particles is investigated from the viewpoint of moving observers. Using a numerical approach, the behavior of the fidelity in terms of the boost parameter is described for different amounts of spin entanglement and momentum entanglement. It is shown that for the spin entangled states the fidelity decreases less than that of the case of spin product states and there are special cases for which the fidelity remains perfect regardless of moving observers’ velocity. Generally, in the limit of boosts with speeds close to the speed of light, the fidelity saturates, i.e., it reaches to a constant value that depends on the amount of momentum entanglement and the width of the momentum distribution function.     

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.     

Perfect quantum information processing with Dicke-class state

We investigate the possibility of implementing perfectquantum information processing with Dicke-class state. It is shownthat the symmetric Dicke state |D_N ^(m)〉 only has themaximal bipartite entanglement of one ebit when N = 2m andgenerally it is not maximally entangled for all bipartitions. Byadjusting the suitable weights and relative phases in the Dickestate |D_N ^(m)〉, we present a class of asymmetric Dickestates \(|\overline D_N^{(m)}\rangle\) which have the maximalbipartite entanglement of q (1 ≤ q ≤ m) ebits. We also obtainthe sufficient and necessary condition that the Dicke-class states\(|\overline D_{N}^{(m)}\rangle\) have the maximal bipartiteentanglement. We illustrate our idea using the four-qubit Dickestate with two excitations. It is shown that our proposedDicke-class states have distinct advantages over the symmetric Dickestate in perfect quantum information processing.     

Entanglement of Fermi gases in a harmonic trap

For both cases with and without interactions, bipartite entanglement of two fermions from a Fermi gas in a trap is investigated. We show how the entanglement depends on the locations of the two fermions and the total particle number of the Fermi gas. Fermions at the edge of trap have longer entanglement distance (beyond it, the entanglement disappears) than those in the center. We derive a lower limitation to the average overlapping for two entangled fermions in the BCS ground state, it is shown to be , a function of Cooper pair number Q and the total number of occupied energy levels M.     

Maximal entanglement of bipartite spin states in the context of quantum algebra

In the framework of the U _q (su(2)) quantum algebra, we investigate the entanglement properties of two-spin systems, of arbitrary spins j ₁ and j ₂, defined in an entanglement of deformed spin coherent states of each of the spins. We derive the amount of entanglement and we give conditions under which bipartite entangled states become maximally entangled. Using these conditions, we construct a large class of Bell states for any choices of the parameters that specify the spin coherent states.     

Quantum Correlations of Two Relativistic Spin-12 Particles Under Noisy Channels

We study the quantum correlation dynamics of bipartite spin-\(\frac {1}{2}\) density matrices for two particles under Wigner rotations induced by Lorentz transformations which is transmitted through noisy channels. We compare quantum entanglement, geometric discord(GD), and quantum discord (QD) for bipartite relativistic spin-\(\frac {1}{2}\) states under noisy channels. We find out QD and GD tend to death asymptotically but a sudden change in the decay rate of the entanglement occurs under noisy channels. Also, bipartite relativistic spin density matrices are considered as a quantum channel for teleportation one-qubit state under the influence of depolarizing noise and compare fidelity for various velocities of observers.     

Mixedness of the N-qubit states with exchange symmetry

The mixedness of the N-qubit quantum states with exchange symmetry has been studied, and the results show that the linear entropy of the single qubit reduced density matrix （RDM）, which can describe the mixedness, is completely determined by the expectation values 〈Sz〉 and 〈S±〉 for both the pure and the mixed states. The mixedness of the pure states can be used to describe the bipartite entanglement, as an example we have calculated the mixedness of the Dicke state and the spin squeezed Kitagawa-Ueda state. For the mixed states, we determine the mixedness properties of both the ground states and the thermal states in mean-field clusters of spin-1/2 particles interacting via the anisotropy Heisenberg XXZ interaction, and found for the ferromagnetic case （J 〈 0）, the mixedness will approximate to the pairwise entanglement when the anisotropic parameter △ 〉 △c.     

Global entanglement and coherent states in an {\sf N}-partite system

We consider a quantum system consisting of N parts, each of which is a “quKit” described by a K dimensional Hilbert space. We prove that in the symmetric subspace, , a pure state is not globally entangled, if and only if it is a coherent state. It is also shown that in the orthogonal complement all states are globally entangled.     

Entanglement of Bipartite Quantum Systems Driven by Repeated Interactions

We consider a non-interacting bipartite quantum system $\mathcal H_S^A\otimes \mathcal H_S^B$ undergoing repeated quantum interactions with an environment modeled by a chain of independent quantum systems interacting one after the other with the bipartite system. The interactions are made so that the pieces of environment interact first with $\mathcal H_S^A$ and then with $\mathcal H_S^B$ . Even though the bipartite systems are not interacting, the interactions with the environment create an entanglement. We show that, in the limit of short interaction times, the environment creates an effective interaction Hamiltonian between the two systems. This interaction Hamiltonian is explicitly computed and we show that it keeps track of the order of the successive interactions with $\mathcal H_S^A$ and $\mathcal H_S^B$ . Particular physical models are studied, where the evolution of the entanglement can be explicitly computed. We also show the property of return of equilibrium and thermalization for a family of examples.     

Some features of the conditional ${\mathsf q}$-entropies of composite quantum systems

The study of conditional q-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The q-entropies depend on the density matrix through the quantity , and admit as a particular instance the standard von Neumann entropy in the limit case . A comprehensive numerical survey of the space of pure and mixed states of bipartite systems is here performed, in order to determine the volumes in state space occupied by those states exhibiting various special properties related to the signs of their conditional q-entropies and to their connections with other separability-related features, including the majorization condition. Different values of the entropic parameter q are considered, as well as different values of the dimensions N ₁ and N ₂ of the Hilbert spaces associated with the constituting subsystems. Special emphasis is paid to the analysis of the monotonicity properties, both as a function of q and as a function of N ₁ and N ₂, of the various entropic functionals considered.Received: 30 May 2003, Published online: 15 October 2003PACS: 03.67.-a Quantum information - 89.70.+c Information theory and communication theory - 03.65.-w Quantum mechanics     

Temperature dependent atomic transport properties of liquid Sn

A simple analytical model for atomic motion of Tankeshwar et al. [J. Phys.: Condens. Matter 3, 3173 (1991)] is used to obtain velocity autocorrelation function (VACF) with the inter-atomic potential and the pair correlation function as required inputs for liquid Sn. For the electron-ion interaction the modified empty-core potential is used, which represents the orthogonalisation effect due to s-core states in such sp-bonded metals. Temperature dependence of structure factor is considered through temperature dependent potential parameter in the pair potential. The coherent behaviour of liquid Sn in terms of the dynamic structure factor employing viscoelastic theory has also been studied. Intrinsic temperature effect has been studied through damping term\hbox{${\exp}( {-\frac{{\pi k}_{{B}} {T}}{{2k}_{{F}} }{r}} )$} exp (?πkBT2kFr)in the pair potential. The predicted results for VACF, cosine power spectrum, mean square displacement, diffusion and viscosity coefficients have been compared with recent available data, and a good agreement has been achieved.     

Decoherence of quantum excitation of even/odd coherent states in thermal environment

In this paper, we study the decoherence of quantum excitation (photon-added) even /odd coherent states, \(((\hat a{^{\dagger }})^{m} \left | {\alpha _ \pm } \right \rangle )\), in a thermal environment by investigating the variation of negative part of the Wigner quasidistribution function vs. the rescaled time. For this purpose, at first we obtain the time-dependent Wigner function corresponding to the mentioned states in the framework of standard master equation. Then, the time evolution of the Wigner function associated with photon-added even /odd coherent states, as well as the number of added photons m are analysed. It is shown that, in both states, the negative part of the Wigner function decreases with time. By deriving the threshold value of the rescaled time for single photon-added even /odd coherent states, it is also found that, if the rescaled time exceeds the threshold value, the associated Wigner function becomes positive, i.e., the decoherence occurs completely.     

Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field

We investigate the phase decoherence effects on the entanglement of a two-qubit anisotropic Heisenberg model with a nonuniform magnetic field in the x–z-plane. As a measure of the entanglement, the concurrence of the system is calculated. It is shown that when the magnetic field is along the z-axis, the nonuniform and uniform components of the field have no influence on the entanglement for the cases of and , respectively. But when the magnetic field is not along the z-axis, both the uniform and the nonuniform components of the field will introduce the decoherence effects. It is found that the effects of the Heisenberg chain's anisotropy in the Z-direction on the entanglement are dependent on the direction of the field. Moreover, the larger the initial concurrence is, the higher value it will exhibit during the time evolution of the system for a proper set of the parameters ν, Δ, θ, γ , B and b.     

Entanglement of superpositions

Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are biorthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one ebit more than the average of the entanglement of the two states being superposed. However, for more general states, the situation is very different.     

Nonclassical Properties for Two Coupled N-Two-Level Atom and a Single Two-Level Atom Under an External Magnetic Field

We study the interaction between a single two-level atom and N two-level atoms under the effect of a uniform magnetic field. The exact solution is obtained and the expectation value of the time-dependent quantum operators calculated using the Block state (the generalized coherent state). We discuss numerically the atomic inversion where the phenomenon of collapse and revival is observed. The change in the value of the atomic angle plays a role in variance squeezing, where it is pronounced for ?? = π/3. Entropy squeezing is discussed and occurred in the first quadrature. The degree of entanglement through linear entropy is examined where the system shows partial entanglement and at a certain value of parameters displays nearly maximum entanglement.     

Teleportation of tripartite entangled coherent states

This paper proposes a feasible scheme for the quantum teleportation of tripartite entangled coherent states by using linear optical devices such as beam splitters, phase shifters and photo detectors. The scheme is based on the bipartite maximally entangled coherent state and the tripartite entangled coherent state with bipartite maximal entanglement as quantum channels. It shows that when the mean number of photons is equal to 2, the total minimum of the average fidelity for an arbitrary tripartite entangled state is 1-0.67×10 ^-3.     

EIT-assisted atomic squeezing

The interaction of classical and quantized electromagnetic fields with an ensemble of atoms in an optical cavity is considered. Four fields drive a double- level scheme in the atoms, consisting of a pair of systems sharing the same set of lower levels. Two of the fields produce maximum coherence, , between the ground state sublevels 1 and 2. This pumping scheme involves equal intensity fields that are resonant with both the one- and two-photon transitions of the system. There is no steady-state absorption of these fields, implying that the fields induce a type Electromagnetically-Induced Transparency (EIT) in the medium. An additional pair of fields interacting with the second system, combined with the EIT fields, leads to squeezing of the atom spin associated with the ground state sublevels. Our method involves a new mechanism for creating steady-state spin squeezing using an optical cavity. As the cooperativity parameter C is increased, the optimal squeezing varies as C ^-1/3. For experimentally accessible values of C, squeezing as large as 90% can be achieved.Received: 28 May 2003, Published online: 12 August 2003PACS: 42.50.Lc Quantum fluctuations, quantum noise, and quantum jumps - 42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements - 42.65.Pc Optical bistability, multistability, and switching, including local field effects     

Retrodiction for coherent communication with homodyne or heterodyne detection

Previous work on the retrodictive theory of direct detection is extended to cover the homodyne detection of coherent optical signal states and . The retrodictive input state probabilities are obtained by the application of Bayes' theorem to the corresponding predictive distributions, based on the probability operator measure (POM) elements for the homodyne process. Results are derived for the retrodictive information on the complex amplitude of the signal field obtainable from the difference photocount statistics of both 4-port and 8-port balanced homodyne detection schemes. The local oscillator is usually assumed much stronger than the signal but the case of equal strengths in 4-port detection is also considered. The calculated probability distributions and error rates are illustrated numerically for values of signal and local oscillator strengths that extend from the classical to the quantum regimes.