19,915 research outputs found
Fundamental limitations in the purifications of tensor networks
We show a fundamental limitation in the description of quantum many-body
mixed states with tensor networks in purification form. Namely, we show that
there exist mixed states which can be represented as a translationally
invariant (TI) matrix product density operator (MPDO) valid for all system
sizes, but for which there does not exist a TI purification valid for all
system sizes. The proof is based on an undecidable problem and on the
uniqueness of canonical forms of matrix product states. The result also holds
for classical states.Comment: v1: 11 pages, 1 figure. v2: very minor changes. About to appear in
Journal of Mathematical Physic
Exponential Separation of Quantum and Classical Online Space Complexity
Although quantum algorithms realizing an exponential time speed-up over the
best known classical algorithms exist, no quantum algorithm is known performing
computation using less space resources than classical algorithms. In this
paper, we study, for the first time explicitly, space-bounded quantum
algorithms for computational problems where the input is given not as a whole,
but bit by bit. We show that there exist such problems that a quantum computer
can solve using exponentially less work space than a classical computer. More
precisely, we introduce a very natural and simple model of a space-bounded
quantum online machine and prove an exponential separation of classical and
quantum online space complexity, in the bounded-error setting and for a total
language. The language we consider is inspired by a communication problem (the
set intersection function) that Buhrman, Cleve and Wigderson used to show an
almost quadratic separation of quantum and classical bounded-error
communication complexity. We prove that, in the framework of online space
complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change
Ergodic versus nonergodic behavior in oxygen deficient high-T_c superconductors
The oxygen defects induced phase transition from nonergodic to ergodic state
in superconductors with intragrain granularity is considered within the
superconductive glass model. The model predictions are found to be in a
qualitative agreement with some experimental observations in deoxygenated
high-T_c single crystals
Systems of Linear Equations over and Problems Parameterized Above Average
In the problem Max Lin, we are given a system of linear equations
with variables over in which each equation is assigned a
positive weight and we wish to find an assignment of values to the variables
that maximizes the excess, which is the total weight of satisfied equations
minus the total weight of falsified equations. Using an algebraic approach, we
obtain a lower bound for the maximum excess.
Max Lin Above Average (Max Lin AA) is a parameterized version of Max Lin
introduced by Mahajan et al. (Proc. IWPEC'06 and J. Comput. Syst. Sci. 75,
2009). In Max Lin AA all weights are integral and we are to decide whether the
maximum excess is at least , where is the parameter.
It is not hard to see that we may assume that no two equations in have
the same left-hand side and . Using our maximum excess results,
we prove that, under these assumptions, Max Lin AA is fixed-parameter tractable
for a wide special case: for an arbitrary fixed function
.
Max -Lin AA is a special case of Max Lin AA, where each equation has at
most variables. In Max Exact -SAT AA we are given a multiset of
clauses on variables such that each clause has variables and asked
whether there is a truth assignment to the variables that satisfies at
least clauses. Using our maximum excess results, we
prove that for each fixed , Max -Lin AA and Max Exact -SAT AA can
be solved in time This improves
-time algorithms for the two problems obtained by Gutin et
al. (IWPEC 2009) and Alon et al. (SODA 2010), respectively
Observation of band structure and density of states effects in Co-based magnetic tunnel junctions
Utilizing Co/AlO/Co magnetic tunnel junctions (MTJs) with Co
electrodes of different crystalline phases, a clear relationship between
electrode structure and junction transport properties is presented. For
junctions with one fcc(111) textured and one polycrystalline (poly-phase and
poly-directional) Co electrode, a strong asymmetry is observed in the
magnetotransport properties, while when both electrodes are polycrystalline the
magnetotransport is essentially symmetric. These observations are successfully
explained within a model based on ballistic tunneling between the calculated
band structures (DOS) of fcc-Co and hcp-Co.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
The Spectral Signature of Dust Scattering and Polarization in the Near IR to Far UV. I. Optical Depth and Geometry Effects
Spectropolarimetry from the near IR to the far UV of light scattered by dust
provides a valuable diagnostic of the dust composition, grain size distribution
and spatial distribution. To facilitate the use of this diagnostic, we present
detailed calculations of the intensity and polarization spectral signature of
light scattered by optically thin and optically thick dust in various
geometries. The polarized light radiative transfer calculations are carried out
using the adding-doubling method for a plane-parallel slab, and are extended to
an optically thick sphere by integrating over its surface. The calculations are
for the Mathis, Rumple & Nordsieck Galactic dust model, and cover the range
from 1 to 500 \AA. We find that the wavelength dependence of the
scattered light intensity provides a sensitive probe of the optical depth of
the scattering medium, while the polarization wavelength dependence provides a
probe of the grain scattering properties, which is practically independent of
optical depth. We provide a detailed set of predictions, including polarization
maps, which can be used to probe the properties of dust through imaging
spectropolarimetry in the near IR to far UV of various Galactic and
extragalactic objects. In a following paper we use the codes developed here to
provide predictions for the dependence of the intensity and polarization on
grain size distribution and composition.Comment: 29 pages + 21 figures, accepted for the Astrophysical Journal
Supplement February 2000 issue. Some revision, mostly in the introduction and
the conclusions, and a couple of correction
Non-standard quantum so(3,2) and its contractions
A full (triangular) quantum deformation of so(3,2) is presented by
considering this algebra as the conformal algebra of the 2+1 dimensional
Minkowskian spacetime. Non-relativistic contractions are analysed and used to
obtain quantum Hopf structures for the conformal algebras of the 2+1 Galilean
and Carroll spacetimes. Relations between the latter and the null-plane quantum
Poincar\'e algebra are studied.Comment: 9 pages, LaTe
Electron Cotunneling in a Semiconductor Quantum Dot
We report transport measurements on a semiconductor quantum dot with a small
number of confined electrons. In the Coulomb blockade regime, conduction is
dominated by cotunneling processes. These can be either elastic or inelastic,
depending on whether they leave the dot in its ground state or drive it into an
excited state, respectively. We are able to discriminate between these two
contributions and show that inelastic events can occur only if the applied bias
exceeds the lowest excitation energy. Implications to energy-level spectroscopy
are discussed.Comment: To be published in Phys. Rev. Let
The Hilbertian Tensor Norm and Entangled Two-Prover Games
We study tensor norms over Banach spaces and their relations to quantum
information theory, in particular their connection with two-prover games. We
consider a version of the Hilbertian tensor norm and its dual
that allow us to consider games with arbitrary output alphabet
sizes. We establish direct-product theorems and prove a generalized
Grothendieck inequality for these tensor norms. Furthermore, we investigate the
connection between the Hilbertian tensor norm and the set of quantum
probability distributions, and show two applications to quantum information
theory: firstly, we give an alternative proof of the perfect parallel
repetition theorem for entangled XOR games; and secondly, we prove a new upper
bound on the ratio between the entangled and the classical value of two-prover
games.Comment: 33 pages, some of the results have been obtained independently in
arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6
rewritten, v3: completely rewritten in order to improve readability; title
changed; references added; published versio
Microscopic Model for Granular Stratification and Segregation
We study segregation and stratification of mixtures of grains differing in
size, shape and material properties poured in two-dimensional silos using a
microscopic lattice model for surface flows of grains. The model incorporates
the dissipation of energy in collisions between rolling and static grains and
an energy barrier describing the geometrical asperities of the grains. We study
the phase diagram of the different morphologies predicted by the model as a
function of the two parameters. We find regions of segregation and
stratification, in agreement with experimental finding, as well as a region of
total mixing.Comment: 4 pages, 7 figures, http://polymer.bu.edu/~hmakse/Home.htm
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