7,832 research outputs found
Order and Disorder in AKLT Antiferromagnets in Three Dimensions
The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a
family of quantum antiferromagnets on arbitrary lattices, where the local spin
S is an integer multiple M of half the lattice coordination number. The equal
time quantum correlations in their ground states may be computed as finite
temperature correlations of a classical O(3) model on the same lattice, where
the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping
implies that all AKLT states are quantum disordered. We consider AKLT states in
d=3 where the nature of the AKLT states is now a question of detail depending
upon the choice of lattice and spin; for sufficiently large S some form of Neel
order is almost inevitable. On the unfrustrated cubic lattice, we find that all
AKLT states are ordered while for the unfrustrated diamond lattice the minimal
S=2 state is disordered while all other states are ordered. On the frustrated
pyrochlore lattice, we find (conservatively) that several states starting with
the minimal S=3 state are disordered. The disordered AKLT models we report here
are a significant addition to the catalog of magnetic Hamiltonians in d=3 with
ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure
Optimized generation of spatial qudits by using a pure phase spatial light modulator
We present a method for preparing arbitrary pure states of spatial qudits,
namely, D-dimensional (D > 2) quantum systems carrying information in the
transverse momentum and position of single photons. For this purpose, a set of
D slits with complex transmission are displayed on a spatial light modulator
(SLM). In a recent work we have shown a method that requires a single
phase-only SLM to control independently the complex coefficients which define
the quantum state of dimension D. The amplitude information was codified by
introducing phase gratings inside each slit and the phase value of the complex
transmission was added to the phase gratings. After a spatial filtering process
we obtained in the image plane the desired qudit state. Although this method
has proven to be a good alternative to compact the previously reported
architectures, it presents some features that could be improved. In this paper
we present an alternative scheme to codify the required phase values that
minimizes the effects of temporal phase fluctuations associated to the SLM
where the codification is carried on. In this scheme the amplitudes are set by
appropriate phase gratings addressed at the SLM while the relative phases are
obtained by a lateral displacement of these phase gratings. We show that this
method improves the quality of the prepared state and provides very high
fidelities of preparation for any state. An additional advantage of this scheme
is that a complete 2\pi modulation is obtained by shifting the grating by one
period, and hence the encoding is not limited by the phase modulation range
achieved by the SLM. Numerical simulations, that take into account the phase
fluctuations, show high fidelities for thousands of qubit states covering the
whole Bloch sphere surface. Similar analysis are performed for qudits with D =
3 and D = 7.Comment: 12 pages, 7 figure
Hybrid automata as coalgebras
Publicado em "Theoretical aspects of computing - ICTAC 2016: 13th International Colloquium, Taipei, Taiwan, ROC, October 24–31, 2016, Proceedings". ISBN 978-3-319-46749-8Able to simultaneously encode discrete transitions and continuous
behaviour, hybrid automata are the de facto framework for the
formal specification and analysis of hybrid systems. The current paper
revisits hybrid automata from a coalgebraic point of view. This allows to
interpret them as state-based components, and provides a uniform theory
to address variability in their definition, as well as the corresponding
notions of behaviour, bisimulation, and observational semantics.FCT grants SFRH/BD/52234/2013, SFRH/BSAB/ 113890/2015ERDF - European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT within project PTDC/EEI-CTP/4836/201
Propagation of spatially entangled qudits through free space
We show the propagation of entangled states of high-dimensional quantum
systems. The qudits states were generated using the transverse correlation of
the twin photons produced by spontaneous parametric down-conversion. Their
free-space distribution was performed at the laboratory scale and the
propagated states maintained a high-fidelity with their original form. The use
of entangled qudits allow an increase in the quantity of information that can
be transmitted and may also guarantee more privacy for communicating parties.
Therefore, studies about propagating entangled states of qudits are important
for the effort of building quantum communication networks.Comment: 5 Pages, 4 Figures, REVTeX
Languages and models for hybrid automata: A coalgebraic perspective
article in pressWe study hybrid automata from a coalgebraic point of view. We show that such a perspective supports a generic theory of hybrid automata with a rich palette of definitions and results. This includes, among other things, notions of bisimulation and behaviour, state minimisation techniques, and regular expression languages.POCI-01-0145-FEDER-016692. RDF — European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation — COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT — Fundação para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-016692 and by the PT-FLAD Chair on Smart Cities & Smart Governance at Universidade do Minh
Modified Gravity on the Brane and Dark Energy
We analyze the dynamics of an AdS5 braneworld with matter fields when gravity
is allowed to deviate from the Einstein form on the brane. We consider exact
5-dimensional warped solutions which are associated with conformal bulk fields
of weight -4 and describe on the brane the following three dynamics: those of
inhomogeneous dust, of generalized dark radiation, and of homogeneous
polytropic dark energy. We show that, with modified gravity on the brane, the
existence of such dynamical geometries requires the presence of non-conformal
matter fields confined to the brane.Comment: Revised version published in Gen. Rel. Grav. Typos corrected, updated
reference and some remarks added for clarity. 11 pages, latex, no figure
Control of quantum transverse correlations on a four-photon system
Control of spatial quantum correlations in bi-photons is one of the
fundamental principles of Quantum Imaging. Up to now, experiments have been
restricted to controlling the state of a single bi-photon, by using linear
optical elements. In this work we demonstrate experimental control of quantum
correlations in a four-photon state comprised of two pairs of photons. Our
scheme is based on a high-efficiency parametric downconversion source coupled
to a double slit by a variable linear optical setup, in order to obtain
spatially encoded qubits. Both entangled and separable pairs have been
obtained, by altering experimental parameters. We show how the correlations
influence both the interference and diffraction on the double slit.Comment: 14 pages, 6 figure
- …