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

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

A q-deformed nonlinear map

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors -- a phenomenon rare in one dimensional maps.Comment: 17 pages, 19 figure

Bilateral native nephrectomy improves renal isograft function in rats

Bilateral native nephrectomy improves renal isograft function in rats. Bilateral native nephrectomy has been suggested to improve renal allograft survival in man. This effect may be most prominent in patients experiencing acute tubular necrosis following transplantation. Thus, native kidneys may alter the course of ischemic acute tubular necrosis in the transplanted kidney. In the present studies, we utilized an experimental model of syngeneic transplantation in which rejection does not occur. We studied Lewis rat renal isografts transplanted into littermates following sham, unilateral or bilateral native nephrectomy. In a fourth group of rats, we evaluated the importance of native kidney excretory function by studying isografts transplanted into littermates with bilaterally obstructed native kidneys. Renal blood flow and excretory function were measured in vivo, eight days following transplantation. Renal excretory function of isografts transplanted into animals following bilateral native nephrectomy was similar to normal nontrans-planted Lewis kidneys. The presence of either one or both functioning native kidneys significantly reduced isograft inulin clearance, PAH clearance, and blood flow. However, when isografts were transplanted into Lewis rats with bilaterally obstructed native kidneys, renal isograft inulin clearance and blood flow were not significantly impaired Non-transplanted kidneys demonstrated “functional hypertrophy” following contralateral nephrectomy, with glomerular filtration rate and renal blood flow increasing by approximately 50%. In contrast, isograft glomerular filtration rate in animals following bilateral native nephrectomy was equivalent to that of single kidneys from normal animals with both kidneys in situ. However, renal blood flow of isografts from these animals increased to the same level as nontransplanted Lewis kidneys following contralateral nephrectomy. Histological examination of isografts from animals with functioning native kidneys in situ demonstrated extensive disruption of normal renal architecture with tubular and interstitial injury. This was in marked contrast to the appearance of Lewis–Brown Norway allografts, to isografts from animals following bilateral native nephrectomy, and to isografts from animals with bilaterally obstructed native kidneys. In Lewis–Brown Norway allografts, there was evidence of rejection with active inflammatory cell infiltration, arteriolitis and venulitis. In isografts from animals following bilateral native nephrectomy or with bilaterally obstructed native kidneys, renal architecture was normal. Thus, the detrimental effect of native kidneys on isograft function may be related to impaired recovery from ischemia or potentiation of ischemic injury which occurs during the transplantation procedure

On the Mixing of the Scalar Mesons f0(1370)f_0(1370), f0(1500)f_0(1500) and f0(1710)f_0(1710)

Based on a $3\times3$ mass matrix describing the mixing of the scalar states $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, the hadronic decays of the three states are investigated. Taking into account the two possible assumptions concerning the mass level order of the bare states $|N>=|u\bar{u}+d\bar{d}>/\sqrt{2}$, $|S>=|s\bar{s}>$ and $|G>=|gg>$ in the scalar sector, $M_G > M_S > M_N$ and $M_G > M_N > M_S$, we obtain the glueball-quarkonia content of the three states by solving the unlinear equations. Some predictions about the decays of the three states in two cases are presented, which can provide a stringent consistency check of the two assumptions.Comment: revtex 10 pages, 1 eps 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

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

Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model

We investigate the entanglement between any two spins in a one dimensional Heisenberg chain as a function of temperature and the external magnetic field. We find that the entanglement in an antiferromagnetic chain can be increased by increasing the temperature or the external field. Increasing the field can also create entanglement between otherwise disentangled spins. This entanglement can be confirmed by testing Bell's inequalities involving any two spins in the solid.Comment: 4 pages, 5 figure

Formal and finite order equivalences

We show that two families of germs of real-analytic subsets in $C^{n}$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of real-analytic self-maps and vector fields under conjugations. On the other hand, we provide an example of two sets of germs of smooth curves that are equivalent of any finite order but not formally equivalent

Multiparticle entanglement with quantum logic networks: Application to cold trapped ions

We show how to construct a multi-qubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other N-1 qubits. We provide an algorithm how to build up an array of networks consisting of single-qubit rotations and multi-qubit control-NOT gates for the synthesis of an arbitrary entangled quantum state of N qubits. We illustrate the algorithm on a system of cold trapped ions. This example illuminates the efficiency of the direct implementation of the multi-qubit CNOT gate compared to its decomposition into a network of two-qubit CNOT gates.Comment: 13 pages, Revtex4, 10 eps figures, 2 tables, to appear in Phys. Rev.