3,179 research outputs found
A complete set of covariants of the four qubit system
We obtain a complete and minimal set of 170 generators for the algebra of
SL(2,\C)^{\times 4}-covariants of a binary quadrilinear form. Interpreted in
terms of a four qubit system, this describes in particular the algebraic
varieties formed by the orbits of local filtering operations in its projective
Hilbert space. Also, this sheds some light on the local unitary invariants, and
provides all the possible building blocks for the construction of entanglement
measures for such a system.Comment: 14 pages, IOP macros; slightly expanded versio
New invariants for entangled states
We propose new algebraic invariants that distinguish and classify entangled
states. Considering qubits as well as higher spin systems, we obtained complete
entanglement classifications for cases that were either unsolved or only
conjectured in the literature.Comment: published versio
Highest weight Macdonald and Jack Polynomials
Fractional quantum Hall states of particles in the lowest Landau levels are
described by multivariate polynomials. The incompressible liquid states when
described on a sphere are fully invariant under the rotation group. Excited
quasiparticle/quasihole states are member of multiplets under the rotation
group and generically there is a nontrivial highest weight member of the
multiplet from which all states can be constructed. Some of the trial states
proposed in the literature belong to classical families of symmetric
polynomials. In this paper we study Macdonald and Jack polynomials that are
highest weight states. For Macdonald polynomials it is a (q,t)-deformation of
the raising angular momentum operator that defines the highest weight
condition. By specialization of the parameters we obtain a classification of
the highest weight Jack polynomials. Our results are valid in the case of
staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio
H-alpha observations of the gamma-ray-emitting Be/X-ray binary LSI+61303: orbital modulation, disk truncation, and long-term variability
We report 138 spectral observations of the H-alpha emission line of the
radio- and gamma-ray-emitting Be/X-ray binary LSI+61303 obtained during the
period of September 1998 -- January 2013. From measuring various H-alpha
parameters, we found that the orbital modulation of the H-alpha is best visible
in the equivalent width ratio EW(B)/EW(R), the equivalent width of the blue
hump, and in the radial velocity of the central dip. The periodogram analysis
confirmed that the H-alpha emission is modulated with the orbital and
superorbital periods. For the past 20 years the radius of the circumstellar
disk is similar to the Roche lobe size at the periastron. It is probably
truncated by a 6:1 resonance. The orbital maximum of the equivalent width of
H-alpha emission peaks after the periastron and coincides on average with the
X-ray and gamma-ray maxima. All the spectra are available upon request from the
authors and through the CDS.Comment: 11 pages, accepted for publication in A&
Vector valued Macdonald polynomials
This paper defines and investigates nonsymmetric Macdonald polynomials with
values in an irreducible module of the Hecke algebra of type . These
polynomials appear as simultaneous eigenfunctions of Cherednik operators.
Several objects and properties are analyzed, such as the canonical bilinear
form which pairs polynomials with those arising from reciprocals of the
original parameters, and the symmetrization of the Macdonald polynomials. The
main tool of the study is the Yang-Baxter graph. We show that these Macdonald
polynomials can be easily computed following this graph. We give also an
interpretation of the symmetrization and the bilinear forms applied to the
Macdonald polynomials in terms of the Yang-Baxter graph.Comment: 85 pages, 5 figure
Phase transition in the Countdown problem
Here we present a combinatorial decision problem, inspired by the celebrated
quiz show called the countdown, that involves the computation of a given target
number T from a set of k randomly chosen integers along with a set of
arithmetic operations. We find that the probability of winning the game
evidences a threshold phenomenon that can be understood in the terms of an
algorithmic phase transition as a function of the set size k. Numerical
simulations show that such probability sharply transitions from zero to one at
some critical value of the control parameter, hence separating the algorithm's
parameter space in different phases. We also find that the system is maximally
efficient close to the critical point. We then derive analytical expressions
that match the numerical results for finite size and permit us to extrapolate
the behavior in the thermodynamic limit.Comment: Submitted for publicatio
Algebraic invariants of five qubits
The Hilbert series of the algebra of polynomial invariants of pure states of
five qubits is obtained, and the simplest invariants are computed.Comment: 4 pages, revtex. Short discussion of quant-ph/0506073 include
Classification of qubit entanglement: SL(2,C) versus SU(2) invariance
The role of SU(2) invariants for the classification of multiparty
entanglement is discussed and exemplified for the Kempe invariant I_5 of pure
three-qubit states. It is found to being an independent invariant only in
presence of both W-type entanglement and threetangle. In this case, constant
I_5 admits for a wide range of both threetangle and concurrences. Furthermore,
the present analysis indicates that an SL^3 orbit of states with equal tangles
but continuously varying I_5 must exist. This means that I_5 provides no
information on the entanglement in the system in addition to that contained in
the tangles (concurrences and threetangle) themselves. Together with the
numerical evidence that I_5 is an entanglement monotone this implies that SU(2)
invariance or the monotone property are too weak requirements for the
characterization and quantification of entanglement for systems of three
qubits, and that SL(2,C) invariance is required. This conclusion can be
extended to general multipartite systems (including higher local dimension)
because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex
The Partition Function of Multicomponent Log-Gases
We give an expression for the partition function of a one-dimensional log-gas
comprised of particles of (possibly) different integer charge at inverse
temperature {\beta} = 1 (restricted to the line in the presence of a
neutralizing field) in terms of the Berezin integral of an associated non-
homogeneous alternating tensor. This is the analog of the de Bruijn integral
identities [3] (for {\beta} = 1 and {\beta} = 4) ensembles extended to
multicomponent ensembles.Comment: 14 page
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