1,946 research outputs found
Spectrum conditions for symmetric extendible states
We analyze bipartite quantum states that admit a symmetric extension. Any
such state can be decomposed into a convex combination of states that allow a
_pure_ symmetric extension. A necessary condition for a state to admit a pure
symmetric extension is that the spectra of the local and global density
matrices are equal. This condition is also sufficient for two qubits, but not
for any larger systems. Using this condition we present a conjectured necessary
and sufficient condition for a two qubit state to admit symmetric extension,
which we prove in some special cases. The results from symmetric extension
carry over to degradable and anti-degradable channels and we use this to prove
that all degradable channels with qubit output have a qubit environment.Comment: 14 pages, 2 figure
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
Computational Difficulty of Computing the Density of States
We study the computational difficulty of computing the ground state
degeneracy and the density of states for local Hamiltonians. We show that the
difficulty of both problems is exactly captured by a class which we call #BQP,
which is the counting version of the quantum complexity class QMA. We show that
#BQP is not harder than its classical counting counterpart #P, which in turn
implies that computing the ground state degeneracy or the density of states for
classical Hamiltonians is just as hard as it is for quantum Hamiltonians.Comment: v2: Accepted version. 9 pages, 1 figur
The computational difficulty of finding MPS ground states
We determine the computational difficulty of finding ground states of
one-dimensional (1D) Hamiltonians which are known to be Matrix Product States
(MPS). To this end, we construct a class of 1D frustration free Hamiltonians
with unique MPS ground states and a polynomial gap above, for which finding the
ground state is at least as hard as factoring. By lifting the requirement of a
unique ground state, we obtain a class for which finding the ground state
solves an NP-complete problem. Therefore, for these Hamiltonians it is not even
possible to certify that the ground state has been found. Our results thus
imply that in order to prove convergence of variational methods over MPS, as
the Density Matrix Renormalization Group, one has to put more requirements than
just MPS ground states and a polynomial spectral gap.Comment: 5 pages. v2: accepted version, Journal-Ref adde
Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
We examine in details the connections between topological and entanglement
properties of short-range resonating valence bond (RVB) wave functions using
Projected Entangled Pair States (PEPS) on kagome and square lattices on
(quasi-)infinite cylinders with generalized boundary conditions (and perimeters
with up to 20 lattice spacings). Making use of disconnected topological sectors
in the space of dimer lattice coverings, we explicitly derive (orthogonal)
"minimally entangled" PEPS RVB states. For the kagome lattice, we obtain, using
the quantum Heisenberg antiferromagnet as a reference model, the finite size
scaling of the energy separations between these states. In particular, we
extract two separate (vanishing) energy scales corresponding (i) to insert a
vison line between the two ends of the cylinder and (ii) to pull out and freeze
a spin at either end. We also investigate the relations between bulk and
boundary properties and show that, for a bipartition of the cylinder, the
boundary Hamiltonian defined on the edge can be written as a product of a
highly non-local projector with an emergent (local) su(2)-invariant
one-dimensional (superfluid) t--J Hamiltonian, which arises due to the symmetry
properties of the auxiliary spins at the edge. This multiplicative structure, a
consequence of the disconnected topological sectors in the space of dimer
lattice coverings, is characteristic of the topological nature of the states.
For minimally entangled RVB states, it is shown that the entanglement spectrum,
which reflects the properties of the edge modes, is a subset (half for kagome
RVB) of the spectrum of the local Hamiltonian, providing e.g. a simple argument
on the origin of the topological entanglement entropy S0=-ln 2 of Z2 spin
liquids. We propose to use these features to probe topological phases in
microscopic Hamiltonians and some results are compared to existing DMRG data.Comment: 15 pages, 19 figures. Large extension of the paper. Finite size
scaling of the (topological) ground state energy splittings added (for the
Kagome quantum antiferromagnet
Refining Chandra/ACIS Subpixel Event Repositioning Using a Backside Illuminated CCD Model
Subpixel event repositioning (SER) techniques have been demonstrated to
significantly improve the already unprecedented spatial resolution of Chandra
X-ray imaging with the Advanced CCD Imaging Spectrometer (ACIS). Chandra CCD
SER techniques are based on the premise that the impact position of events can
be refined, based on the distribution of charge among affected CCD pixels. ACIS
SER models proposed thus far are restricted to corner split (3- and 4-pixel)
events, and assume that such events take place at the split pixel corners. To
improve the event counting statistics, we modified the ACIS SER algorithms to
include 2-pixel split events and single pixel events, using refined estimates
for photon impact locations. Furthermore, simulations that make use of a
high-fidelity backside illuminated (BI) CCD model demonstrate that mean photon
impact positions for split events are energy dependent leading to further
modification of subpixel event locations according to event type and energy,
for BI ACIS devices. Testing on Chandra CCD X-ray observations of the Orion
Nebula Cluster indicates that these modified SER algorithms further improve the
spatial resolution of Chandra/ACIS, to the extent that the spreading in the
spatial distribution of photons is dominated by the High Resolution Mirror
Assembly, rather than by ACIS pixelization.Comment: 23 pages, 8 figures, 2nd version, submitted to Ap
Matrix Product State and mean field solutions for one-dimensional systems can be found efficiently
We consider the problem of approximating ground states of one-dimensional
quantum systems within the two most common variational ansatzes, namely the
mean field ansatz and Matrix Product States. We show that both for mean field
and for Matrix Product States of fixed bond dimension, the optimal solutions
can be found in a way which is provably efficient (i.e., scales polynomially).
This implies that the corresponding variational methods can be in principle
recast in a way which scales provably polynomially. Moreover, our findings
imply that ground states of one-dimensional commuting Hamiltonians can be found
efficiently.Comment: 5 pages; v2: accepted version, Journal-ref adde
Lifetime Adherence to Physical Activity Recommendations and Fall Occurrence in Community-dwelling Older Adults: a Retrospective Cohort Study
Falling is a major health concern for community-dwelling older adults. Regular physical activity has been proposed to prevent falls. The aim of this study was to assess whether the achievement of the 2004 UK Department of Health physical activity recommendations over a lifetime had a protective effect against falling in older people. 313 community-dwelling older adults completed a questionnaire about lifetime physical activity and fall occurrence. There were significantly fewer falls in those who had led an active lifestyle compared to those who had not (χ2Yates=4.568, p=0.033), with a lower relative risk of fall occurrence for the active respondents (RR=0.671) compared to the inactive (RR=1.210). Of those who were sufficiently active in their early adulthood, the decade where there was the biggest decrease in remaining active enough was in the 60s. It is concluded that an active lifestyle may have decreased the likelihood of having a fall in older ag
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