38 research outputs found
Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions
We provide quantitative bounds on the characterisation of multiparticle
separable states by states that have locally symmetric extensions. The bounds
are derived from two-particle bounds and relate to recent studies on quantum
versions of de Finetti's theorem. We discuss algorithmic applications of our
results, in particular a quasipolynomial-time algorithm to decide whether a
multiparticle quantum state is separable or entangled (for constant number of
particles and constant error in the LOCC or Frobenius norm). Our results
provide a theoretical justification for the use of the Search for Symmetric
Extensions as a practical test for multiparticle entanglement.Comment: 5 pages, 1 figur
Geometric discord and Measurement-induced nonlocality for well known bound entangled states
We employ geometric discord and measurement induced nonlocality to quantify
non classical correlations of some well-known bipartite bound entangled states,
namely the two families of Horodecki's (, and
dimensional) bound entangled states and that of Bennett etal's in
dimension. In most of the cases our results are analytic and both
the measures attain relatively small value. The amount of quantumness in the
bound entangled state of Benatti etal and the state
having the same matrix representation (in computational basis) is same.
Coincidently, the Werner and isotropic states also exhibit the
same property, when seen as dimensional states.Comment: V2: Title changed, one more state added; 11 pages (single column), 2
figures, accepted in Quantum Information Processin
Measurement of Angular Distributions and R= sigma_L/sigma_T in Diffractive Electroproduction of rho^0 Mesons
Production and decay angular distributions were extracted from measurements
of exclusive electroproduction of the rho^0(770) meson over a range in the
virtual photon negative four-momentum squared 0.5< Q^2 <4 GeV^2 and the
photon-nucleon invariant mass range 3.8< W <6.5 GeV. The experiment was
performed with the HERMES spectrometer, using a longitudinally polarized
positron beam and a ^3He gas target internal to the HERA e^{+-} storage ring.
The event sample combines rho^0 mesons produced incoherently off individual
nucleons and coherently off the nucleus as a whole. The distributions in one
production angle and two angles describing the rho^0 -> pi+ pi- decay yielded
measurements of eight elements of the spin-density matrix, including one that
had not been measured before. The results are consistent with the dominance of
helicity-conserving amplitudes and natural parity exchange. The improved
precision achieved at 47 GeV,
reveals evidence for an energy dependence in the ratio R of the longitudinal to
transverse cross sections at constant Q^2.Comment: 15 pages, 15 embedded figures, LaTeX for SVJour(epj) document class
Revision: Fig. 15 corrected, recent data added to Figs. 10,12,14,15; minor
changes to tex
Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities
Employing Hilbert-Schmidt measure, we explicitly compute and analyze a number
of determinantal product (bivariate) moments |rho|^k |rho^{PT}|^n,
k,n=0,1,2,3,..., PT denoting partial transpose, for both generic
(9-dimensional) two-rebit (alpha = 1/2) and generic (15-dimensional) two-qubit
(alpha=1) density matrices rho. The results are, then, incorporated by Dunkl
into a general formula (Appendix D6), parameterized by k, n and alpha, with the
case alpha=2, presumptively corresponding to generic (27-dimensional)
quaternionic systems. Holding the Dyson-index-like parameter alpha fixed, the
induced univariate moments (|rho| |rho^{PT}|)^n and |rho^{PT}|^n are inputted
into a Legendre-polynomial-based (least-squares) probability-distribution
reconstruction algorithm of Provost (Mathematica J., 9, 727 (2005)), yielding
alpha-specific separability probability estimates. Since, as the number of
inputted moments grows, estimates based on |rho| |rho^{PT}| strongly decrease,
while ones employing |rho^{PT}| strongly increase (and converge faster), the
gaps between upper and lower estimates diminish, yielding sharper and sharper
bounds. Remarkably, for alpha = 2, with the use of 2,325 moments, a
separability-probability lower-bound 0.999999987 as large as 26/323 = 0.0804954
is found. For alpha=1, based on 2,415 moments, a lower bound results that is
0.999997066 times as large as 8/33 = 0.242424, a (simpler still) fractional
value that had previously been conjectured (J. Phys. A, 40, 14279 (2007)).
Furthermore, for alpha = 1/2, employing 3,310 moments, the lower bound is
0.999955 times as large as 29/64 = 0.453125, a rational value previously
considered (J. Phys. A, 43, 195302 (2010)).Comment: 47 pages, 12 figures; slightly expanded and modified for journal
publication; this paper incorporates and greatly extends arXiv:1104.021