Quantum nonlocality test for continuous-variable states with dichotomic observables

There have been theoretical and experimental studies on quantum nonlocality for continuous variables, based on dichotomic observables. In particular, we are interested in two cases of dichotomic observables for the light field of continuous variables: One case is even and odd numbers of photons and the other case is no photon and the presence of photons. We analyze various observables to give the maximum violation of Bell's inequalities for continuous-variable states. We discuss an observable which gives the violation of Bell's inequality for any entangled pure continuous-variable state. However, it does not have to be a maximally entangled state to give the maximal violation of Bell's inequality. This is attributed to a generic problem of testing the quantum nonlocality of an infinite- dimensional state using a dichotomic observable.

Experimentally realizable characterizations of continuous- variable Gaussian states

Measures of entanglement, fidelity, and purity are basic yardsticks in quantum-information processing. We propose how to implement these measures using linear devices and homodyne detectors for continuous-variable Gaussian states. In particular, the test of entanglement becomes simple with some prior knowledge that is relevant to current experiments.

Quantum homogenization for continuous variables: Realization with linear optical elements

Recently Ziman et al. [Phys. Rev. A 65, 042105 (2002)] have introduced a concept of a universal quantum homogenizer which is a quantum machine that takes as input a given (system) qubit initially in an arbitrary state rho and a set of N reservoir qubits initially prepared in the state xi. The homogenizer realizes, in the limit sense, the transformation such that at the output each qubit is in an arbitrarily small neighborhood of the state xi irrespective of the initial states of the system and the reservoir qubits. In this paper we generalize the concept of quantum homogenization for qudits, that is, for d-dimensional quantum systems. We prove that the partial-swap operation induces a contractive map with the fixed point which is the original state of the reservoir. We propose an optical realization of the quantum homogenization for Gaussian states. We prove that an incoming state of a photon field is homogenized in an array of beam splitters. Using Simon's criterion, we study entanglement between outgoing beams from beam splitters. We derive an inseparability condition for a pair of output beams as a function of the degree of squeezing in input beams.

Entanglement transfer from continuous variables to qubits

We show that two qubits can be entangled by local interactions with an entangled two-mode continuous variable state. This is illustrated by the evolution of two two-level atoms interacting with a two-mode squeezed state. Two modes of the squeezed field are injected respectively into two spatially separate cavities and the atoms are then sent into the cavities to interact resonantly with the cavity field. We find that the atoms may be entangled even by a two-mode squeezed state which has been decohered while penetrating into the cavity.

Continuous MLL-ENL expression is necessary to establish a "Hox Code" and maintain immortalization of hematopoietic progenitor cells

The t[(11;19)(p22;q23)] translocation, which gives rise to the MLL-ENL fusion protein, is commonly found in infant acute leukemias of both the myeloid and lymphoid lineage. To investigate the molecular mechanism of immortalization by MLL-ENL we established a Tet-regulatable system of MLL-ENL expression in primary hematopoietic progenitor cells. Immortalized myeloid cell lines were generated, which are dependent on continued MLL-ENL expression for their survival and proliferation. These cells either terminally differentiate or die when MLL-ENL expression is turned off with doxycycline. The expression profile of all 39 murine Hox genes was analyzed in these cells by real-time quantitative PCR. This analysis showed that loss of MLL-ENL was accompanied by a reduction in the expression of multiple Hoxa genes. By comparing these changes with Hox gene expression in cells induced to differentiate with granulocyte colony-stimulating factor, we show for the first time that reduced Hox gene expression is specific to loss of MLL-ENL and is not a consequence of differentiation. Our data also suggest that the Hox cofactor Meis-2 can substitute for Meis-1 function. Thus, MLL-ENL is required to initiate and maintain immortalization of myeloid progenitors and may contribute to leukemogenesis by aberrantly sustaining the expression of a "Hox code" consisting of Hoxa4 to Hoxa11.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Distribution-based adaptive bounding genetic algorithm for continuous optimisation problems

A new search-space-updating technique for genetic algorithms is proposed for continuous optimisation problems. Other than gradually reducing the search space during the evolution process with a fixed reduction rate set ‘a priori’, the upper and the lower boundaries for each variable in the objective function are dynamically adjusted based on its distribution statistics. To test the effectiveness, the technique is applied to a number of benchmark optimisation problems in comparison with three other techniques, namely the genetic algorithms with parameter space size adjustment (GAPSSA) technique [A.B. Djurišic, Elite genetic algorithms with adaptive mutations for solving continuous optimization problems – application to modeling of the optical constants of solids, Optics Communications 151 (1998) 147–159], successive zooming genetic algorithm (SZGA) [Y. Kwon, S. Kwon, S. Jin, J. Kim, Convergence enhanced genetic algorithm with successive zooming method for solving continuous optimization problems, Computers and Structures 81 (2003) 1715–1725] and a simple GA. The tests show that for well-posed problems, existing search space updating techniques perform well in terms of convergence speed and solution precision however, for some ill-posed problems these techniques are statistically inferior to a simple GA. All the tests show that the proposed new search space update technique is statistically superior to its counterparts.