Multipartite entanglement and quantum state exchange

We investigate multipartite entanglement in relation to the process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some 2N-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a measure called the entanglement of minimum bipartite entropy.

Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity

A semiconductor based scheme has been proposed for generating entangled photon pairs from the radiative decay of an electrically pumped biexciton in a quantum dot. Symmetric dots produce polarization entanglement, but experimentally realized asymmetric dots produce photons entangled in both polarization and frequency. In this work, we investigate the possibility of erasing the “which-path” information contained in the frequencies of the photons produced by asymmetric quantum dots to recover polarization-entangled photons. We consider a biexciton with nondegenerate intermediate excitonic states in a leaky optical cavity with pairs of degenerate cavity modes close to the nondegenerate exciton transition frequencies. An open quantum system approach is used to compute the polarization entanglement of the two-photon state after it escapes from the cavity, measured by the visibility of two-photon interference fringes. We explicitly relate the two-photon visibility to the degree of the Bell-inequality violation, deriving a threshold at which Bell-inequality violations will be observed. Our results show that an ideal cavity will produce maximally polarization-entangled photon pairs, and even a nonideal cavity will produce partially entangled photon pairs capable of violating a Bell-inequality.

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the dimension of the Hilbert space of the system under study. This is a square-root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2/2)(k)((1)) and current superalgebra. osp(2/2)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2/2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2/2)(k)((1)) in the standard basis are obtained for arbitrary level k. (C) 2004 Elsevier B.V. All rights reserved.

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Exact solution of the XXZ Gaudin model with generic open boundaries

The XXZ Gaudin model with generic integrable boundaries specified by generic non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. (C) 2004 Elsevier B.V. All rights reserved.

Braided m-Lie algebras

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End(F)M, where M is a Yetter-Drinfeld module over B with dimB < infinity. In particular, generalized classical braided m-Lie algebras sl(q,f)(GM(G)(A),F) and osp(q,l)(GM(G)(A),M,F) of generalized matrix algebra GMG(A) are constructed and their connection with special generalized matrix Lie superalgebra sl(s,f)(GM(Z2)(A(s)),F) and orthosymplectic generalized matrix Lie super algebra osp(s,l) (GM(Z2)(A(s)),M-s,F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.

Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

Optical quantum computation using cluster states

We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beam splitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantum computing proposal of Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)], and the abstract cluster-state model of quantum computation proposed by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)].

Gaussian quantum Monte Carlo methods for fermions and bosons

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.