23,004 research outputs found
A mathematical foundation of quantum information and quantum computer -on quantum mutual entropy and entanglement-
The study of mutual entropy (information) and capacity in classica l system
was extensively done after Shannon by several authors like Kolmogor ov and
Gelfand. In quantum systems, there have been several definitions of t he mutual
entropy for classical input and quantum output. In 1983, the autho r defined
the fully quantum mechanical mutual entropy by means of the relati ve entropy
of Umegaki, and it has been used to compute the capacity of quant um channel
for quantum communication process; quantum input-quantum output.
Recently, a correlated state in quantum syatems, so-called quantum entangled
state or quantum entanglement, are used to study quntum information, in part
icular, quantum computation, quantum teleportation, quantum cryptography.
In this paper, we mainly discuss three things below: (1) We point out the di
fference between the capacity of quantum channel and that of classical-quant
um-classical channel. (2) So far the entangled state is merely defined as a
non-separable state, we give a wider definition of the entangled state and c
lassify the entangled states into three categories. (3) The quantum mutual e
ntropy for an entangled state is discussed. The above (2) and (3) are a join t
work with Belavkin.Comment: 10 pages, Latex2
Numerical approach to SUSY quantum mechanics and the gauge/gravity duality
We demonstrate that Monte-Carlo simulation is a practical tool to study
nonperturbative aspects of supersymmetric quantum mechanics. As an example we
study D0-brane quantum mechanics in the context of superstring theory.
Numerical data nicely reproduce predictions from gravity side, including the
coupling constant dependence of the string alpha' correction. This strongly
suggests the duality to hold beyond the supergravity approximation. Although
detail of the stringy correction cannot be obtained by state-of-the-art
techniques in gravity side, in the matrix quantum mechanics we can obtain
concrete values. Therefore the Monte-Carlo simulation combined with the duality
provides a powerful tool to study the superstring theory.Comment: 16 pages, 4 figures. Based on an invited talk at the workshop
"Supersymmetric Quantum Mechanics and Spectral Design", Benasque, Spain,
2010, Jul 18 -- Jul 3
Relation between high-energy quasiparticles of quasi-one-dimensional antiferromagnets in a magnetic field and a doublon of a Hubbard chain
In spin-1/2 one-dimensional Heisenberg antiferromagnets and anisotropic
triangular Heisenberg antiferromagnets, high-energy states carrying
considerable spectral weights have been observed in a magnetic field using
inelastic neutron scattering. Such high-energy properties cannot be explained
in terms of either Nambu-Goldstone bosons due to spontaneous breaking of
continuous symmetries or quasiparticles in a Tomonaga-Luttinger liquid. Here,
we show that the mechanism causing the high-energy states is analogous to that
of the upper Hubbard band in the one-dimensional Hubbard model, by
theoretically tracing the origin of the high-energy states back to string
solutions of the Bethe ansatz.Comment: 6 pages, 1 figur
On the ampleness of positive CR line bundles over Levi-flat manifolds
We give an example of a compact Levi-flat CR 3-manifold with a
positive-along-leaves CR line bundle which is not ample with respect to
transversely infinitely differentiable CR sections. This example shows that we
cannot improve the regularity of Kodaira type embedding theorem for compact
Levi-flat CR manifolds obtained by Ohsawa and Sibony.Comment: 12 pages, final version, to appear in Publications of the Research
Institute for Mathematical Science
Fermi-LAT observations of GRBs with weak LAT emission
We present the analysis results of three Gamma-Ray Bursts (GRBs) detected by
the Gamma-ray Burst Monitor (GBM) and the Large Area Telescope (LAT) onboard
Fermi: the two long GRB 080825C and GRB 090217, and the first short burst with
GeV photons GRB 081024B. The emission from GRB 081024B observed by the LAT
above 100 MeV is delayed with respect to the GBM trigger, and significantly
extends after the low-energy episode. Some hints for spectral hardening was
observed in this burst as well as in GRB 080825C, possibly related to a
separate and harder component showing up at late times. Conversely, GRB 090217
does not exhibit any noticeable feature. Together with the other bright LAT
detected bursts (e.g. GRB 080916C and GRB 090510), these observations help to
classify the GRB properties and give new insight on the acceleration mechanisms
responsible for their emission at the highest energies.Comment: 2009 Fermi Symposium. eConf Proceedings C09112
Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals
We introduce the concept of index for regular Dirichlet forms by means of
energy measures, and discuss its properties. In particular, it is proved that
the index of strong local regular Dirichlet forms is identical with the
martingale dimension of the associated diffusion processes. As an application,
a class of self-similar fractals is taken up as an underlying space. We prove
that first-order derivatives can be defined for functions in the domain of the
Dirichlet forms and their total energies are represented as the square
integrals of the derivatives.Comment: 33 pages, 3 figure
Large-Nc equivalence and the sign problem at finite baryon density
QCD with a finite baryon chemical potential, despite its importance, is not
well understood because the standard lattice QCD simulation is not applicable
due to the sign problem. Although QCD-like theories which do not suffer from
the sign problem have been studied intensively, relation to QCD with a finite
baryon chemical potential was not clear. This paper introduces large-
equivalences between QCD and various QCD-like theories. These equivalences lead
us to a unified viewpoint for QCD with baryon and isospin chemical potentials,
and gauge theories, QCD with adjoint matters and
two-color QCD. In particular QCD with the baryon chemical potential is
large- equivalent to its phase quenched version in a certain parameter
region, which is relevant for heavy ion collision experiments. All previous
simulation results which study the effect of the phase confirm the phase quench
approximation is quantitatively good already at Nc=3; it is so good that often
two theories give the same value within error. Therefore the phase quenched
simulation is the best strategy for the QCD critical point search. At small
volume one can study a tiny 1/Nc effect by the phase reweighting; the large-Nc
equivalence guarantees that the phase reweighing method works without suffering
from the overlapping problem.Comment: Slightly modified version of the article submitted to Seitaro
Nakamura competition. 23 pages, 9 figures. v2: 25 pages, 9 figure
On dlog image of K_2 of elliptic surface minus singular fibers
Modular section addedComment: 60 page
Ground State Properties of the Two-Dimensional t-J Model
The two-dimensional - model in the ground state is investigated by the
power Lanczos method. The pairing-pairing correlation function for
-wave symmetry is enhanced in the realistic parameter regime for
high- superconductors. The charge susceptibility shows divergent
behavior as near half-filling for the doping
concentration , indicating that the value of the dynamical exponent
is four under the assumption of hyperscaling. The peak height of the spin
structure factor also behaves as
near half-filling, which leads to the divergence of the antiferromagnetic
correlation length as . The boundary of
phase separation is estimated on the basis of the Maxwell construction.
Numerical results are compared with experimental features observed in
high- cuprates.Comment: 15 pages, RevTex, 12 PostScript figures, to appear in Phys.Rev.
Proposed experiment on the continuity of quantum entanglement
We propose experiments on quantum entanglement for investigating the Einstein
Podolsky Rosen (EPR) problem with the polarization directions of photons. These
experiments are performed to investigate whether the defined polarization
directions in an entangled state are teleported between entangled photons.
EPR-type sequential experiments are performed using a twin-photon beam and two
pairs of linear polarization analyzers under the cross-Nicol condition (i.e.,
orthogonal to each other). If the third filter whose polarization angle is 45
degrees is set between the first cross-Nicol filters, the beam intensity is
changed from 0 to 12.5 %, and at the second cross-Nicol filters, the beam
intensity is changed from 0 to 25 %. In this experiment, we predict that the
"continuity of quantum entanglement" under a pure Hamiltonian evolution is
detected.Comment: 6 pages, 5 figure
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