20 research outputs found
On quantum mean-field models and their quantum annealing
This paper deals with fully-connected mean-field models of quantum spins with
p-body ferromagnetic interactions and a transverse field. For p=2 this
corresponds to the quantum Curie-Weiss model (a special case of the
Lipkin-Meshkov-Glick model) which exhibits a second-order phase transition,
while for p>2 the transition is first order. We provide a refined analytical
description both of the static and of the dynamic properties of these models.
In particular we obtain analytically the exponential rate of decay of the gap
at the first-order transition. We also study the slow annealing from the pure
transverse field to the pure ferromagnet (and vice versa) and discuss the
effect of the first-order transition and of the spinodal limit of metastability
on the residual excitation energy, both for finite and exponentially divergent
annealing times. In the quantum computation perspective this quantity would
assess the efficiency of the quantum adiabatic procedure as an approximation
algorithm.Comment: 44 pages, 23 figure
Faithful Squashed Entanglement
Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published
version, claims have been weakened from the LOCC norm to the one-way LOCC
nor
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
Geometric Measures of Quantum Correlations with Bures and Hellinger Distances
This article contains a survey of the geometric approach to quantum
correlations. We focus mainly on the geometric measures of quantum correlations
based on the Bures and quantum Hellinger distances.Comment: to be published as a chapter of the book "Lectures on general quantum
correlations and their applications" edited by F. Fanchini, D. Soares-Pinto,
and G. Adesso (Springer, 2017); 47 pages, 3 figures; second version: minor
typos in the first version correcte