8,156 research outputs found
Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems
We seek to derive the probability--expressed in terms of the Hilbert-Schmidt
(Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit
system is separable, by implementing the well-known Peres-Horodecki test on the
partial transposes (PT's) of the associated 4 x 4 density matrices). But the
full implementation of the test--requiring that the determinant of the PT be
nonnegative for separability to hold--appears to be, at least presently,
computationally intractable. So, we have previously implemented--using the
auxiliary concept of a diagonal-entry-parameterized separability function
(DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal
minors of the PT. This yielded an exact upper bound on the separability
probability of 1024/{135 pi^2} =0.76854$. Here, we piece together
(reflection-symmetric) results obtained by requiring that each of the four 3 x
3 principal minors of the PT, in turn, be nonnegative, giving an
improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a
still further improved upper bound of 1129/2100 = 0.537619 can be found by
similarly piecing together the (reflection-symmetric) results of enforcing the
simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors.
In deriving our improved upper bounds, we rely repeatedly upon the use of
certain integrals over cubes that arise. Finally, we apply an independence
assumption to a pair of DESF's that comes close to reproducing our numerical
estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the
end are correcte
Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional
and 15-dimensional in nature, respectively. The total volumes of the spaces
they occupy with respect to the Hilbert-Schmidt and Bures metrics are
obtainable as special cases of formulas of Zyczkowski and Sommers. We claim
that if one could determine certain metric-independent 3-dimensional
"eigenvalue-parameterized separability functions" (EPSFs), then these formulas
could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes
occupied by only the separable two-qubit states (and hence associated
separability probabilities). Motivated by analogous earlier analyses of
"diagonal-entry-parameterized separability functions", we further explore the
possibility that such 3-dimensional EPSFs might, in turn, be expressible as
univariate functions of some special relevant variable--which we hypothesize to
be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical
results we obtain are rather closely supportive of this hypothesis. Both the
real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude
roughly 50% at C=1/2, as well as a number of additional matching
discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.
d1005+68: A New Faint Dwarf Galaxy in the M81 Group
We present the discovery of d1005+68, a new faint dwarf galaxy in the M81
Group, using observations taken with the Subaru Hyper Suprime-Cam. d1005+68's
color-magnitude diagram is consistent with a distance of
Mpc, establishing group membership. We derive an absolute -band magnitude,
from stellar isochrone fitting, of , with a
half-light radius of pc. These place d1005+68 within
the radius-luminosity locus of Local Group and M81 satellites and among the
faintest confirmed satellites outside the Local Group. Assuming an age of 12
Gyr, d1005+68's red giant branch is best fit by an isochrone of [Fe/H] . It has a projected separation from nearby M81 satellite BK5N of only
5 kpc. As this is well within BK5N's virial radius, we speculate that d1005+68
may be a satellite of BK5N. If confirmed, this would make d1005+68 one of the
first detected satellites-of-a-satellite.Comment: 7 pages, 4 figures, 1 table, additional affiliations include
Andromeda XXIX: A New Dwarf Spheroidal Galaxy 200 kpc from Andromeda
We report the discovery of a new dwarf galaxy, Andromeda XXIX (And XXIX), using data from the recently released Sloan Digital Sky Survey Data Release 8, and confirmed by Gemini North telescope Multi-Object Spectrograph imaging data. And XXIX appears to be a dwarf spheroidal galaxy, separated on the sky by a little more than 15° from M31, with a distance inferred from the tip of the red giant branch of 730 ± 75 kpc, corresponding to a three-dimensional separation from M31 of 207 +20 – 2 kpc (close to M31's virial radius). Its absolute magnitude, as determined by comparison to the red giant branch luminosity function of the Draco dwarf spheroidal, is M V = –8.3 ± 0.4. And XXIX's stellar populations appear very similar to Draco's; consequently, we estimate a metallicity for And XXIX of [Fe/H] ~–1.8. The half-light radius of And XXIX is 360 ± 60 pc and its ellipticity is 0.35 ± 0.06, typical of dwarf satellites of the Milky Way and M31 at this absolute magnitude range.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90744/1/2041-8205_742_1_L15.pd
Andromeda XXVIII: A Dwarf Galaxy More Than 350 kpc from Andromeda
We report the discovery of a new dwarf galaxy, Andromeda XXVIII, using data
from the recently-released SDSS DR8. The galaxy is a likely satellite of
Andromeda, and, at a separation of kpc, would be one of the
most distant of Andromeda's satellites. Its heliocentric distance is
kpc, and analysis of its structure and luminosity show that
it has an absolute magnitude of and half-light
radius of pc, similar to many other faint Local Group
dwarfs. With presently-available imaging we are unable to determine if there is
ongoing or recent star formation, which prevents us from classifying it as a
dwarf spheroidal or dwarf irregular.Comment: Accepted to ApJ Letter
Price Discovery and the Accuracy of Consolidated Data Feeds in the U.S. Equity Markets
Both the scientific community and the popular press have paid much attention
to the speed of the Securities Information Processor, the data feed
consolidating all trades and quotes across the US stock market. Rather than the
speed of the Securities Information Processor, or SIP, we focus here on its
accuracy. Relying on Trade and Quote data, we provide various measures of SIP
latency relative to high-speed data feeds between exchanges, known as direct
feeds. We use first differences to highlight not only the divergence between
the direct feeds and the SIP, but also the fundamental inaccuracy of the SIP.
We find that as many as 60 percent or more of trades are reported out of
sequence for stocks with high trade volume, therefore skewing simple measures
such as returns. While not yet definitive, this analysis supports our
preliminary conclusion that the underlying infrastructure of the SIP is
currently unable to keep pace with the trading activity in today's stock
market.Comment: 18 pages, 20 figures, 2 table
Theory for Magnetic Anisotropy of Field-Induced Insulator-to-Metal Transition in Cubic Kondo Insulator YbB_{12}
Magnetization and energy gap of Kondo insulator YbB_{12} are calculated
theoretically based on the previously proposed tight-binding model composed of
Yb 5d and 4f orbitals. It is found that magnetization
curves are almost isotropic, naturally expected from the cubic symmetry, but
that the gap-closing field has an anisotropy: the gap closes faster for the
field in (100) direction than in (110) and (111) directions, in accord with the
experiments. This is qualitatively understood by considering the maximal
eigenvalues of the total angular momentum operators projected on each direction
of the magnetic field. But the numerical calculation based on the band model
yields better agreement with the experiment.Comment: 4 pages, 4 figures, to appear in J. Phys. Soc. Jp
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