New approach for analyzing time evolution of density operator in a dissipative channel by the entangled state representation

We analyze the time evolution of mixed state ρ₀ in a dissipative channel, characteristic of a decay constant κ, by virtue of the elegant properties of entangled state representation 〈η|. We find that the matrix element of the mixed state ρ(t) at time t in 〈η| representation is proportional to that of the initial ρ₀ in the decayed entangled state 〈ηe^-κt| representation, accompanying with a Gaussian damping factor . Thus we have a new insight about the nature of the dissipative process.     

A General Method of Selecting Quantum Channel for Bidirectional Quantum Teleportation

Based on tensor representation and Bell basis measurement in bidirectional quantum teleportation, a criterion that can be used to judge whether a four-qubit quantum state can be regarded as quantum channel or not in bidirectional teleportation is suggested and a theoretical scheme of bidirectional teleportation via four-qubit state as the quantum channel is proposed. In accordance with this criterion we give a general method of selecting quantum channel in bidirectional teleportation, which is determined by the channel parameter matrix R in the Bell basis measurement. This general method provide a theoretical basis for quantum channel selection in bidirectional quantum teleportation experiments.     

Classical and quantum statistical mechanics in a common Liouville space

It is shown that the extremal phase-space representations of quantum mechanics can be expressed in terms of wave-functions on L²-spaces which are embedded in L²(Γ). In L²(Γ) all these representations are restrictions of a globally defined representation of the canonical commutation relations. The master Liouville space $\text{B}$²(Γ) over L²(Γ) can accommodate representations of both classical and quantum statistical mechanics, and serves as a medium for their comparison. As a specific example, a Boltzmann-type equation on $\text{B}$²(Γ) is considered in the classical as well as quantum context.     

Nonlinear Channels of Werner States

We study the nonlinear positive map of the density matrix of two-qubit Werner states, called the nonlinear channel. The map ρ → Φ(ρ) is realized by the rational function Φ. We discuss the influence of the map on the entanglement properties of the transformed density matrix. We investigate the violation of the Bell inequality (CHSH inequality) for the two-qubit state Φ(ρ). The nonlinear channels under discussion create the entangled state from a separable Werner state. We study the quantum spin tomograms of the states.     

Precise detection of multipartite entanglement in fourqubit Greenberger–Horne–Zeilinger diagonal states

We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger–Horne–Zeilinger (GHZ) diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.     

Separable State Decompositions for a Class of Mixed States

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n×n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT.     

The ground state of two-dimensional electrons in a nonuniform magnetic field

An exact solution to the Schrödinger equation for the ground state of two-dimensional Pauli electrons in a nonuniform transverse magnetic field H is presented for two cases. In the first case, the field H depends on a single variable, H = H(y), while in the second case, the field is axially symmetric, H = H(ρ), ρ²=x ²+y ². The electron density distributions n = n(y) and n = n(ρ) that correspond to a completely filled lower level are found. For quasiuniform fields of fixed sign, the functions n(y) and n(ρ) are locally related to the magnetic field: n(y) = H(y)/?₀ and n(ρ) = H(ρ)/?₀, where ?₀ = hc/|e| is a magnetic flux quantum. Magnetic fields are considered that are periodic, singular, and bounded in the plane xy. Finite electron objects in a nonuniform magnetic field are analyzed.     

On the Distribution of the Wave Function for Systems in Thermal Equilibrium

For a quantum system, a density matrix ρ that is not pure can arise, via averaging, from a distribution μ of its wave function, a normalized vector belonging to its Hilbert space ?. While ρ itself does not determine a unique μ, additional facts, such as that the system has come to thermal equilibrium, might. It is thus not unreasonable to ask, which μ, if any, corresponds to a given thermodynamic ensemble? To answer this question we construct, for any given density matrix ρ, a natural measure on the unit sphere in ?, denoted GAP(ρ). We do this using a suitable projection of the Gaussian measure on ? with covariance ρ. We establish some nice properties of GAP(ρ) and show that this measure arises naturally when considering macroscopic systems. In particular, we argue that it is the most appropriate choice for systems in thermal equilibrium, described by the canonical ensemble density matrix ρ_β = (1/Z) exp (?β H). GAP(ρ) may also be relevant to quantum chaos and to the stochastic evolution of open quantum systems, where distributions on ? are often used.     

Current Fluctuations in the One-Dimensional Symmetric Exclusion Process with Open Boundaries

We calculate the first four cumulants of the integrated current of the one-dimensional symmetric simple exclusion process of N sites with open boundary conditions. For large system size N, the generating function of the integrated current depends on the densities ρ _a and ρ _b of the two reservoirs and on the fugacity z, the parameter conjugated to the integrated current, through a single parameter. Based on our expressions for these first four cumulants, we make a conjecture which leads to a prediction for all the higher cumulants. In the case ρ _a =1 and ρ _b =0, our conjecture gives the same universal distribution as the one obtained by Lee, Levitov, and Yakovets for one-dimensional quantum conductors in the metallic regime.     

A convergent expansion about mean field theory: I. The expansion

We give a convergent expansion for nearly Gaussian quantum field theory in the multiphase region. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. We study in detail the ground state of the $\text{P}$(φ)₂ = (λφ⁴ ? φ² ? μφ)₂ model, with ∥ μ ∥ ? λ² ? 1. The ground state is close to the classical free field, obtained by replacing $\text{P}$(φ) by the quadratic mean field polynomial $\text{P}$_c(φ), tangent to $\text{P}$ at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. We also establish analyticity in λ for μ = 0 in the sector ∥ Im λ ∥ < ? Re λ ? 1, for ? ? 1.     

Measurement of the spectral functions of vector current hadronic tau decays

A measurement of the spectral functions of non-strange τ vector current final states is presented, using 124 358 τ pairs recorded by the ALEPH detector at LEP during the years 1991 to 1994. The spectral functions of the dominant two- and four-pion τ decay channels are compared to published results of e ⁺ e ^- annihilation experiments via isospin rotation. A combined fit of the pion form factor from τ decays and e ⁺ e ^- data is performed using different parametrizations. The mass and the width of the ρ ^±(770) and the ρ ⁰(770) are separately determined in order to extract possible isospin violating effects. The mass and width differences are measured to be M _ρ ^± ₍₇₇₀₎ - M _ρ ⁰ ₍₇₇₀₎ = (0.0 ± 1.0) MeV/c ² and Γ _ρ ^± ₍₇₇₀₎ - Γ _ρ ⁰ ₍₇₇₀₎ = (0.1 ± 1.9) MeV/c ².     

Laplace operator and hodge decomposition for quantum groups and quantum spaces

LetΓ=Γ _±,z be one of theN ²-dimensional bicovariant first order differential calculi for the quantum groups GL _q (N), SL _q (N), SO _q (N), or Sp _q (N), whereq is a transcendental complex number andz is a regular parameter. It is shown that the de Rham cohomology of Woronowicz’s external algebraΓ ^{^} coincides with the de Rham cohomologies of its leftinvariant, its right-invariant and its biinvariant subcomplexes. In the cases GL _q (N) and SL _q (N) the cohomology ring is isomorphic to the biinvariant external algebraΓ _inv ^{^} and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. It is also applicable for quantum Euclidean spheres. The eigenvalues of the Laplace-Beltrami operator in cases of the general linear quantum group, the orthogonal quantum group, and the quantum Euclidean spheres are given.     

Quantum Entanglement and Reduced Density Matrices

We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.     

Temperature dependence of the rho-meson mass and width

It is shown, to leading order in the virial expansion, that unitarity of the ππ scattering amplitude implies that if the ρ-meson widthΓ _ρ(T) increases with temperature, then the ρ-meson massM _ρ(T) must also increase. The temperature dependence ofM _ρ(T) is explicitly obtained from a simple, but physically motivated, parametrization of theI=J=1 ππ scattering amplitude.     

On the representation theory of quantum Heisenberg group and algebra

We show that the quantum Heisenberg groupH _q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU _q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU _q (h(1)). We derive left and right regular representations forU _q (h(1)) as acting on its dualH _q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. By duality, left and right regular representations for quantum Heisenberg group with the quantum Heisenberg algebra as representation module are also constructed. As before reduction of group left representations leads to finite dimensional irreducible ones for which the intertwinning operator is also investigated.     

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.     

Angular dependence of the upper critical field in Bi2Sr2CuO6+δ

The angular dependence of the upper critical magnetic field was investigated in a wide range of temperatures in very high-quality Bi₂Sr₂CuO_6+δ single crystals with critical temperature T _c (midpoint) ? 9 K in magnetic fields up to 28 T. Although the typical value of the normal state resistivity ratio ρ_c/ρ_ab≈10⁴, the anisotropy ratio H _c2∥ab/H _c2⊥ab of the upper critical fields is much smaller and shows an unexpected temperature dependence. A model based on strong anisotropy and small transparency between superconducting layers is proposed.     

Single-particle approximation to the canonical density operator of a system of N interacting fermions

A necessary condition for the minimum of free energy Tr(ρH^N) + β^-1 Tr(ρlnρ) is investigated for a system of N interacting fermions on the set of all density matrices of the form ρ=Z^-1 exp(-βNΓ^N₁h¹), where Γ^N₁ is Kummer's (1,N)-expansion map, and h¹ is a finite- dimensional one-particle operator. It is shown that for values of β in an open circle $\text{C}\text{(0,β}{}_0\text{)}$ in the complex plane there exists a unique bounded analytic in β one-particle operator X¹(β) such that Z^-1exp(-βNΓ^N₁X¹(β)) satisfies this condition.