116 research outputs found
Partial separability revisited: Necessary and sufficient criteria
We extend the classification of mixed states of quantum systems composed of
arbitrary number of subsystems of arbitrary dimensions. This extended
classification is complete in the sense of partial separability and gives
1+18+1 partial separability classes in the tripartite case contrary to a former
1+8+1. Then we give necessary and sufficient criteria for these classes, which
make it possible to determine to which class a mixed state belongs. These
criteria are given by convex roof extensions of functions defined on pure
states. In the special case of three-qubit systems, we define a different set
of such functions with the help of the Freudenthal triple system approach of
three-qubit entanglement.Comment: v3: 22 pages, 5 tables, 1 figure, minor corrections (typos),
clarification in the Introduction. Accepted in Phys. Rev. A. Comments are
welcom
STU Black Holes as Four Qubit Systems
In this paper we describe the structure of extremal stationary spherically
symmetric black hole solutions in the STU model of D=4, N=2 supergravity in
terms of four-qubit systems. Our analysis extends the results of previous
investigations based on three qubits. The basic idea facilitating this
four-qubit interpretation is the fact that stationary solutions in D=4
supergravity can be described by dimensional reduction along the time
direction. In this D=3 picture the global symmetry group
of the model is extended by the Ehlers SL(2,R) accounting for the fourth qubit.
We introduce a four qubit state depending on the charges (electric, magnetic
and NUT) the moduli and the warp factor. We relate the entanglement properties
of this state to different classes of black hole solutions in the STU model. In
the terminology of four qubit entanglement extremal black hole solutions
correspond to nilpotent, and nonextremal ones to semisimple states. In arriving
at this entanglement based scenario the role of the four algebraically
independent four qubit SL(2,C) invariants is emphasized.Comment: 47 pages LATE
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
We solve the loop equations of the -ensemble model analogously to the
solution found for the Hermitian matrices . For \beta=1y^2=U(x)\beta((\hbar\partial)^2-U(x))\psi(x)=0\hbar\propto
(\sqrt\beta-1/\sqrt\beta)/Ny^2-U(x)[y,x]=\hbarF_h-expansion at arbitrary . The set of "flat"
coordinates comprises the potential times and the occupation numbers
\widetilde{\epsilon}_\alpha\mathcal F_0\widetilde{\epsilon}_\alpha$.Comment: 58 pages, 7 figure
Best network chirplet-chain: Near-optimal coherent detection of unmodeled gravitation wave chirps with a network of detectors
The searches of impulsive gravitational waves (GW) in the data of the
ground-based interferometers focus essentially on two types of waveforms: short
unmodeled bursts and chirps from inspiralling compact binaries. There is room
for other types of searches based on different models. Our objective is to fill
this gap. More specifically, we are interested in GW chirps with an arbitrary
phase/frequency vs. time evolution. These unmodeled GW chirps may be considered
as the generic signature of orbiting/spinning sources. We expect quasi-periodic
nature of the waveform to be preserved independent of the physics which governs
the source motion. Several methods have been introduced to address the
detection of unmodeled chirps using the data of a single detector. Those
include the best chirplet chain (BCC) algorithm introduced by the authors. In
the next years, several detectors will be in operation. The joint coherent
analysis of GW by multiple detectors can improve the sight horizon, the
estimation of the source location and the wave polarization angles. Here, we
extend the BCC search to the multiple detector case. The method amounts to
searching for salient paths in the combined time-frequency representation of
two synthetic streams. The latter are time-series which combine the data from
each detector linearly in such a way that all the GW signatures received are
added constructively. We give a proof of principle for the full sky blind
search in a simplified situation which shows that the joint estimation of the
source sky location and chirp frequency is possible.Comment: 22 pages, revtex4, 6 figure
Covariant Affine Integral Quantization(s)
Covariant affine integral quantization of the half-plane is studied and
applied to the motion of a particle on the half-line. We examine the
consequences of different quantizer operators built from weight functions on
the half-plane. To illustrate the procedure, we examine two particular choices
of the weight function, yielding thermal density operators and affine inversion
respectively. The former gives rise to a temperature-dependent probability
distribution on the half-plane whereas the later yields the usual canonical
quantization and a quasi-probability distribution (affine Wigner function)
which is real, marginal in both momentum p and position q.Comment: 36 pages, 10 figure
On The Universality Class Of Little String Theories
We propose that Little String Theories in six dimensions are quasilocal
quantum field theories. Such field theories obey a modification of Wightman
axioms which allows Wightman functions (i.e. vacuum expectation values of
products of fundamental fields) to grow exponentially in momentum space.
Wightman functions of quasilocal fields in x-space violate microlocality at
short distances. With additional assumptions about the ultraviolet behavior of
quasilocal fields, one can define approximately local observables associated to
big enough compact regions. The minimum size of such a region can be
interpreted as the minimum distance which observables can probe. We argue that
for Little String Theories this distance is of order {\sqrt N}/M_s.Comment: 25 pages, late
Point massive particle in General Relativity
It is well known that the Schwarzschild solution describes the gravitational
field outside compact spherically symmetric mass distribution in General
Relativity. In particular, it describes the gravitational field outside a point
particle. Nevertheless, what is the exact solution of Einstein's equations with
-type source corresponding to a point particle is not known. In the
present paper, we prove that the Schwarzschild solution in isotropic
coordinates is the asymptotically flat static spherically symmetric solution of
Einstein's equations with -type energy-momentum tensor corresponding to
a point particle. Solution of Einstein's equations is understood in the
generalized sense after integration with a test function. Metric components are
locally integrable functions for which nonlinear Einstein's equations are
mathematically defined. The Schwarzschild solution in isotropic coordinates is
locally isometric to the Schwarzschild solution in Schwarzschild coordinates
but differs essentially globally. It is topologically trivial neglecting the
world line of a point particle. Gravity attraction at large distances is
replaced by repulsion at the particle neighbourhood.Comment: 15 pages, references added, 1 figur
Fermions and Kaluza-Klein vacuum decay: a toy model
We address the question of whether or not fermions with twisted periodicity
condition suppress the semiclassical decay of M^4xS^1 Kaluza--Klein vacuum. We
consider a toy (1+1)-dimensional model with twisted fermions in cigar-shaped
Euclidean background geometry and calculate the fermion determinant. We find
that contrary to expectations, the determinant is finite. We consider this as
an indication that twisted fermions do not stabilize the Kaluza--Klein vacuum.Comment: 13 pages, 2 figure
On the curvature of vortex moduli spaces
We use algebraic topology to investigate local curvature properties of the
moduli spaces of gauged vortices on a closed Riemann surface. After computing
the homotopy type of the universal cover of the moduli spaces (which are
symmetric powers of the surface), we prove that, for genus g>1, the holomorphic
bisectional curvature of the vortex metrics cannot always be nonnegative in the
multivortex case, and this property extends to all Kaehler metrics on certain
symmetric powers. Our result rules out an established and natural conjecture on
the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.
Twisted convolution and Moyal star product of generalized functions
We consider nuclear function spaces on which the Weyl-Heisenberg group acts
continuously and study the basic properties of the twisted convolution product
of the functions with the dual space elements. The final theorem characterizes
the corresponding algebra of convolution multipliers and shows that it contains
all sufficiently rapidly decreasing functionals in the dual space.
Consequently, we obtain a general description of the Moyal multiplier algebra
of the Fourier-transformed space. The results extend the Weyl symbol calculus
beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure
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