28,027 research outputs found
Generalised monogamy relation of convex-roof extended negativity in multi-level systems
In this paper, we investigate the generalised monogamy inequalities of
convex-roof extended negativity (CREN) in multi-level systems. The generalised
monogamy inequalities provide the upper and lower bounds of bipartite
entanglement, which are obtained by using CREN and the CREN of assistance
(CRENOA). Furthermore, we show that the CREN of multi-qubit pure states
satisfies some monogamy relations. Additionally, we test the generalised
monogamy inequalities for qudits by considering the partially coherent
superposition of a generalised W-class state in a vacuum and show that the
generalised monogamy inequalities are satisfied in this case as well.Comment: 11 pages, 1 figures. We thank the anonymous referees for their
valuable comments, especially for they corrected a mistike of the Theorem 1
in the first versio
Theoretical Perspective of Convergence Complexity of Evolutionary Algorithms Adopting Optimal Mixing
The optimal mixing evolutionary algorithms (OMEAs) have recently drawn much
attention for their robustness, small size of required population, and
efficiency in terms of number of function evaluations (NFE). In this paper, the
performances and behaviors of OMEAs are studied by investigating the mechanism
of optimal mixing (OM), the variation operator in OMEAs, under two scenarios --
one-layer and two-layer masks. For the case of one-layer masks, the required
population size is derived from the viewpoint of initial supply, while the
convergence time is derived by analyzing the progress of sub-solution growth.
NFE is then asymptotically bounded with rational probability by estimating the
probability of performing evaluations. For the case of two-layer masks,
empirical results indicate that the required population size is proportional to
both the degree of cross competition and the results from the one-layer-mask
case. The derived models also indicate that population sizing is decided by
initial supply when disjoint masks are adopted, that the high selection
pressure imposed by OM makes the composition of sub-problems impact little on
NFE, and that the population size requirement for two-layer masks increases
with the reverse-growth probability.Comment: 8 pages, 2015 GECCO oral pape
General Monogamy of Tsallis -Entropy Entanglement in Multiqubit Systems
In this paper, we study the monogamy inequality of Tsallis-q entropy
entanglement. We first provide an analytic formula of Tsallis-q entropy
entanglement in two-qubit systems for The analytic formula of Tsallis-q entropy
entanglement in system is also obtained and we show that Tsallis-q
entropy entanglement satisfies a set of hierarchical monogamy equalities.
Furthermore, we prove the squared Tsallis-q entropy entanglement follows a
general inequality in the qubit systems. Based on the monogamy relations, a set
of multipartite entanglement indicators is constructed, which can detect all
genuine multiqubit entangled states even in the case of -tangle vanishes.
Moreover, we study some examples in multipartite higher-dimensional system for
the monogamy inequalities.Comment: 9 pages, 12 figures. v3: closed to published versio
Symplectic Divisorial Capping in Dimension 4
We investigate the notion of symplectic divisorial compactification for
symplectic 4-manifolds with either convex or concave type boundary. This is
motivated by the notion of compactifying divisors for open algebraic surfaces.
We give a sufficient and necessary criterion, which is simple and also works in
higher dimensions, to determine whether an arbitrarily small concave/convex
neighborhood exist for an -orthogonal symplectic divisor (a symplectic
plumbing). If deformation of symplectic form is allowed, we show that a
symplectic divisor has either a concave or convex neighborhood whenever the
symplectic form is exact on the boundary of its plumbing. As an application, we
classify symplectic compactifying divisors having finite boundary fundamental
group. We also obtain a finiteness result of fillings when the boundary can be
capped by a symplectic divisor with finite boundary fundamental group.Comment: 66 pages. More complete results obtained. Comments welcome
Some Sufficient Conditions for Finding a Nesting of the Normalized Matching Posets of Rank 3
Given a graded poset , consider a chain decomposition of
. If implies that the set of the ranks of elements in
is a subset of the ranks of elements in for any chains , then we say is a nested chain decomposition (or
nesting, for short) of , and is said to be nested. In 1970s, Griggs
conjectured that every normalized matching rank-unimodal poset is nested. This
conjecture is proved to be true only for all posets of rank 2 [W:05], some
posets of rank 3 [HLS:09,ENSST:11], and the very special cases for higher
ranks. For general cases, it is still widely open. In this paper, we provide
some sufficient conditions on the rank numbers of posets of rank 3 to satisfies
the Griggs's conjecuture.Comment: 8 pages, 2 figure
On The Birch and Swinnerton-Dyer Conjecture for CM Elliptic Curves over \BQ
For CM elliptic curve over rational field with analytic rank one, for any
potential good ordinary prime p, not dividing the number of roots of unity in
the complex multiplication field, we show the p-part of its Shafarevich-Tate
group has order predicted by the Birch and Swinnerton-Dyer conjecture
Generation of vortices and stabilization of vortex lattices in holographic superfluids
Within the simplest holographic superfluid model and without any ingredients
put by hand, it is shown that vortices can be generated when the angular
velocity of rotating superfluids exceeds certain critical values, which can be
precisely determined by linear perturbation analyses (quasi-normal modes of the
bulk AdS black brane). These vortices appear at the edge of the superfluid
system first, and then automatically move into the bulk of the system, where
they are eventually stabilized into certain vortex lattices. For the case of 18
vortices generated, we find (at least) five different patterns of the final
lattices formed due to different initial perturbations, which can be compared
to the known result for such lattices in weakly coupled Bose-Einstein
condensates from free energy analyses
Entanglement bound for multipartite pure states based on local measurements
An entanglement bound based on local measurements is introduced for
multipartite pure states. It is the upper bound of the geometric measure and
the relative entropy of entanglement. It is the lower bound of minimal
measurement entropy. For pure bipartite states, the bound is equal to the
entanglement entropy. The bound is applied to pure tripartite qubit states and
the exact tripartite relative entropy of entanglement is obtained for a wide
class of states.Comment: 8 pages, 1 figure, accepted by Physical Review
Periodically Driven Holographic Superconductor
As a first step towards our holographic investigation of the
far-from-equilibrium physics of periodically driven systems at strong coupling,
we explore the real time dynamics of holographic superconductor driven by a
monochromatically alternating electric field with various frequencies. As a
result, our holographic superconductor is driven to the final oscillating
state, where the condensate is suppressed and the oscillation frequency is
controlled by twice of the driving frequency. In particular, in the large
frequency limit, the three distinct channels towards the final steady state are
found, namely under damped to superconducting phase, over damped to
superconducting and normal phase, which can be captured essentially by the low
lying spectrum of quasi-normal modes in the time averaged approximation,
reminiscent of the effective field theory perspective.Comment: JHEP style, 1+18 pages, 10 figures, version to appear in JHE
Entanglement and genuine entanglement of three qubit GHZ diagonal states
We analytically prove the necessary and sufficient criterion for the full
separability of three-qubit Greenberger-Horne-Zeilinger (GHZ) diagonal states.
The corresponding entanglement is exactly calculable for some GHZ diagonal
states and is tractable for the others using the relative entropy of
entanglement. We show that the biseparable criterion and the genuine
entanglement are determined only by the biggest GHZ diagonal element regardless
of all the other smaller diagonal elements. We have completely solved the
entanglement problems of three-qubit GHZ diagonal states.Comment: 5 pages, 1 figure
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