SpMyb functions as an intramodular repressor to regulate spatial expression of CyIIIa in sea urchin embryos

The CyIIIa actin gene of Strongylocentrotus purpuratus is transcribed exclusively in the embryonic aboral ectoderm, under the control of 2.3 kb cis-regulatory domain that contains a proximal module that controls expression in early embryogenesis, and a middle module that controls expression in later embryogenesis. Previous studies demonstrated that the SpRunt-1 target site within the middle module is required for the sharp increase in CyIIIa transcription which accompanies differentiation of the aboral ectoderm, and that a negative regulatory region near the SpRunt-1 target site is required to prevent ectopic transcription in the oral ectoderm and skeletogenic mesenchyme. This negative regulatory region contains a consensus binding site for the myb family of transcription factors. In vitro DNA-binding experiments reveal that a protein in blastula-stage nuclei interacts specifically with the myb target site. Gene transfer experiments utilizing CyIIIa reporter constructs containing oligonucleotide substitutions indicate that this site is both necessary and sufficient to prevent ectopic expression of CyIIIa. Synthetic oligonucleotides containing the myb target site were used to purify a protein from sea urchin embryo nuclear extracts by affinity chromatography. This protein is immunoprecipitated by antibodies specific to the evolutionarily conserved myb domain, and amino acid sequences obtained from the purified protein were found to be identical to sequences within the myb domain. Sequence information was used to obtain cDNA clones of SpMyb, the S. purpuratus member of the myb family of transcription factors. Through interactions within the middle module, SpMyb functions to repress activation of CyIIIa in the oral ectoderm and skeletogenic mesenchyme

Local symmetry properties of pure 3-qubit states

Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.Comment: 32 pages, 5 encapsulated PostScript files for 3 figures. Published version, with minor correction

On local invariants of pure three-qubit states

We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of degree less than or equal to 6, and find such a set with maximum degree 8. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (non-polynomial) invariants associated with it.Comment: LateX, 13 pages. Minor typoes corrected. Published versio

Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived explicitly. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.Comment: Two figs. Accepted for publication, Journal of Statistical Physic

Entanglement sharing among qudits

Consider a system consisting of n d-dimensional quantum particles (qudits), and suppose that we want to optimize the entanglement between each pair. One can ask the following basic question regarding the sharing of entanglement: what is the largest possible value Emax(n,d) of the minimum entanglement between any two particles in the system? (Here we take the entanglement of formation as our measure of entanglement.) For n=3 and d=2, that is, for a system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper we consider first a system of d qudits and show that Emax(d,d) is greater than or equal to 1. We then consider a system of three particles, with three different values of d. Our results for the three-particle case suggest that as the dimension d increases, the particles can share a greater fraction of their entanglement capacity.Comment: 4 pages; v2 contains a new result for 3 qudits with d=

Localized Entanglement in one-dimensional Anderson model

The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder significantly reduces the average entanglement, and entanglement distribution clearly displays the entanglement localization. The maximal pairwise entanglement exhibits a maximum as the disorder strength increases,experiencing a transition from increase to decrease. The entanglement between the center of localization and other site decreases exponentially along the spatial direction. Finally,we study effects of disorder on dynamical properties of entanglement.Comment: 5 pages, 6 figure

Entanglement molecules

We investigate the entanglement properties of multiparticle systems, concentrating on the case where the entanglement is robust against disposal of particles. Two qubits -belonging to a multipartite system- are entangled in this sense iff their reduced density matrix is entangled. We introduce a family of multiqubit states, for which one can choose for any pair of qubits independently whether they should be entangled or not as well as the relative strength of the entanglement, thus providing the possibility to construct all kinds of ''Entanglement molecules''. For some particular configurations, we also give the maximal amount of entanglement achievable.Comment: 4 pages, 1 figur

Moments of generalized Husimi distributions and complexity of many-body quantum states

We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to the systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution.Comment: published version, 33 pages, 7 figre

Three-qubit pure-state canonical forms

In this paper we analyze the canonical forms into which any pure three-qubit state can be cast. The minimal forms, i.e. the ones with the minimal number of product states built from local bases, are also presented and lead to a complete classification of pure three-qubit states. This classification is related to the values of the polynomial invariants under local unitary transformations by a one-to-one correspondence.Comment: REVTEX, 9 pages, 1 figur

A bipartite class of entanglement monotones for N-qubit pure states

We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems. They therefore capture new information on the non-local properties of multipartite systems.Comment: 6 page