97 research outputs found
Superqubits
We provide a supersymmetric generalization of n quantum bits by extending the
local operations and classical communication entanglement equivalence group
[SU(2)]^n to the supergroup [uOSp(1|2)]^n and the stochastic local operations
and classical communication equivalence group [SL(2,C)]^n to the supergroup
[OSp(1|2)]^n. We introduce the appropriate supersymmetric generalizations of
the conventional entanglement measures for the cases of and . In
particular, super-Greenberger-Horne-Zeilinger states are characterized by a
nonvanishing superhyperdeterminant.Comment: 16 pages, 4 figures, 4 tables, revtex; minor corrections, version
appearing in Phys. Rev.
Wrapped branes as qubits
Recent work has established a correspondence between the tripartite
entanglement measure of three qubits and the macroscopic entropy of the
four-dimensional 8-charge STU black hole of supergravity. Here we consider the
configurations of intersecting D3-branes, whose wrapping around the six compact
dimensions T^6 provides the microscopic string-theoretic interpretation of the
charges, and associate the three-qubit basis vectors |ABC>, (A,B,C=0 or 1) with
the corresponding 8 wrapping cycles. In particular, we relate a well-known fact
of quantum information theory, that the most general real three-qubit state can
be parameterized by four real numbers and an angle, to a well-known fact of
string theory, that the most general STU black hole can be described by four
D3-branes intersecting at an angle.Comment: Version appearing in Phys. Rev. Lett, includes Type IIA description
as well as Type II
Four-qubit entanglement from string theory
We invoke the black hole/qubit correspondence to derive the classification of
four-qubit entanglement. The U-duality orbits resulting from timelike reduction
of string theory from D=4 to D=3 yield 31 entanglement families, which reduce
to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references
adde
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Alginate nanoparticles protect ferrous from oxidation: Potential iron delivery system
A novel, efficient delivery system for iron (Fe²⁺) was developed using the alginate biopolymer. Iron loaded alginate nanoparticles were synthesized by a controlled ionic gelation method and was characterized with respect to particle size, zeta potential, morphology and encapsulation efficiency. Successful loading was confirmed with Fourier Transform Infrared spectroscopy and Thermogravimetric Analysis. Electron energy loss spectroscopy study corroborated the loading of ferrous into the alginate nanoparticles. Iron encapsulation (70%) was optimized at 0.06% Fe (w/v) leading to the formation of iron loaded alginate nanoparticles with a size range of 15-30nm and with a negative zeta potential (-38mV). The in vitro release studies showed a prolonged release profile for 96h. Release of iron was around 65-70% at pH of 6 and 7.4 whereas it was less than 20% at pH 2.The initial burst release upto 8h followed zero order kinetics at all three pH values. All the release profiles beyond 8h best fitted the Korsmeyer-Peppas model of diffusion. Non Fickian diffusion was observed at pH 6 and 7.4 while at pH 2 Fickian diffusion was observed.This research was financially supported by the HETC QIG Win 3 grant, University of Peradeniya, Peradeniya, Sri Lanka
Black holes admitting a Freudenthal dual
The quantised charges x of four dimensional stringy black holes may be
assigned to elements of an integral Freudenthal triple system whose
automorphism group is the corresponding U-duality and whose U-invariant quartic
norm Delta(x) determines the lowest order entropy. Here we introduce a
Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although
distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the
requirement that \tilde{x} be integer restricts us to the subset of black holes
for which Delta(x) is necessarily a perfect square. The issue of higher-order
corrections remains open as some, but not all, of the discrete U-duality
invariants are Freudenthal invariant. Similarly, the quantised charges A of
five dimensional black holes and strings may be assigned to elements of an
integral Jordan algebra, whose cubic norm N(A) determines the lowest order
entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a
perfect cube, for which A**=A and which leaves N(A) invariant. The two
dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde
Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity
One would often like to know when two a priori distinct extremal black
p-brane solutions are in fact U-duality related. In the classical supergravity
limit the answer for a large class of theories has been known for some time.
However, in the full quantum theory the U-duality group is broken to a discrete
subgroup and the question of U-duality orbits in this case is a nuanced matter.
In the present work we address this issue in the context of N=8 supergravity in
four, five and six dimensions. The purpose of this note is to present and
clarify what is currently known about these discrete orbits while at the same
time filling in some of the details not yet appearing in the literature. To
this end we exploit the mathematical framework of integral Jordan algebras and
Freudenthal triple systems. The charge vector of the dyonic black string in D=6
is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified
by a set of two arithmetic U-duality invariants. Similarly, the black hole
(string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge
canonical form, again uniquely fixed by a set of three arithmetic U-duality
invariants. The situation in four dimensions is less clear: while black holes
preserving more than 1/8 of the supersymmetries may be fully classified by
known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield
increasingly subtle orbit structures, which remain to be properly understood.
However, for the very special subclass of projective black holes a complete
classification is known. All projective black holes are E_{7(7)}(Z) related to
a four or five charge canonical form determined uniquely by the set of known
arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the
charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to
appear in Class. Quantum Gra
Freudenthal triple classification of three-qubit entanglement
We show that the three-qubit entanglement classes: (0) Null, (1) Separable
A-B-C, (2a) Biseparable A-BC, (2b) Biseparable B-CA, (2c) Biseparable C-AB, (3)
W and (4) GHZ correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3 and 4 of a
Freudenthal triple system defined over the Jordan algebra C+C+C. We also
compute the corresponding SLOCC orbits.Comment: 11 pages, 2 figures, 6 tables, revtex; minor corrections, references
added; version appearing in Phys. Rev.
Black Holes, Qubits and Octonions
We review the recently established relationships between black hole entropy
in string theory and the quantum entanglement of qubits and qutrits in quantum
information theory. The first example is provided by the measure of the
tripartite entanglement of three qubits, known as the 3-tangle, and the entropy
of the 8-charge STU black hole of N=2 supergravity, both of which are given by
the [SL(2)]^3 invariant hyperdeterminant, a quantity first introduced by Cayley
in 1845. There are further relationships between the attractor mechanism and
local distillation protocols. At the microscopic level, the black holes are
described by intersecting D3-branes whose wrapping around the six compact
dimensions T^6 provides the string-theoretic interpretation of the charges and
we associate the three-qubit basis vectors, |ABC> (A,B,C=0 or 1), with the
corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to
the 56 charge N=8 black holes and the tripartite entanglement of seven qubits
where the measure is provided by Cartan's E_7 supset [SL(2)]^7 invariant. The
qubits are naturally described by the seven vertices ABCDEFG of the Fano plane,
which provides the multiplication table of the seven imaginary octonions,
reflecting the fact that E_7 has a natural structure of an O-graded algebra.
This in turn provides a novel imaginary octonionic interpretation of the 56=7 x
8 charges of N=8: the 24=3 x 8 NS-NS charges correspond to the three imaginary
quaternions and the 32=4 x 8 R-R to the four complementary imaginary octonions.
N=8 black holes (or black strings) in five dimensions are also related to the
bipartite entanglement of three qutrits (3-state systems), where the analogous
measure is Cartan's E_6 supset [SL(3)]^3 invariant.Comment: Version to appear in Physics Reports, including previously omitted
new results on small STU black hole charge orbits and expanded bibliography.
145 pages, 15 figures, 41 table
Spatial and temporal facies evolution of a Lower Jurassic carbonate platform, NW Tethyan margin (Mallorca, Spain)
The variety of depositional facies of a Lower Jurassic carbonate platform has been investigated on the island of Mallorca along a transect comprising six stratigraphic profiles. Twenty-nine facies and sub-facies have been recognized, grouped into seven facies associations, ranging in depositional environment from supratidal/terrestrial and peritidal to outer platform. Spatial and temporal (2D) facies distribution along the transect reflects the evolution of the carbonate platform with time showing different facies associations, from a broad peritidal platform (stage 1) to a muddy open platform (stage 2), and finally to a peritidal to outer carbonate platform (stage 3). Stage 1 (early Sinemurian to earliest late Sinemurian) corresponds to a nearly-flat peritidal-shallow subtidal epicontinental platform with facies belts that shifted far and fast over the whole study area. The evolution from stage 1 to stage 2 (late Sinemurian) represents a rapid flooding of the epicontinental shallow platform, with more open-marine conditions, and the onset of differential subsidence. During stage 3 (latest Sinemurian), peritidal and shallow-platform environments preferentially developed to the northeast (Llevant Mountains domain) with a rapid transition to middle-outer platform environments toward the northwest (Tramuntana Range domain). Stages 1 and 3 present facies associations typical of Bahamian-type carbonates, whereas stage 2 represents the demise of the Bahamian-type carbonate factory and proliferation of muddy substrates with suspension-feeders. The described platform evolution responded to the interplay between the initial extensional tectonic phases related to Early Jurassic Tethyan rifting, contemporaneous environmental perturbations, and progressive platform flooding related to the Late Triassic–Early Jurassic worldwide marine transgression and associated accommodation changes
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