170 research outputs found
Exact dimer ground states for a continuous family of quantum spin chains
Using the matrix product formalism, we define a multi-parameter family of
spin models on one dimensional chains, with nearest and next-nearest neighbor
anti-ferromagnetic interaction for which exact analytical expressions can be
found for its doubly degenerate ground states. The family of Hamiltonians which
we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a
particular point in this parameter space. Like the Majumdar-Ghosh model, the
doubly degenerate ground states of our models have a very simple structure,
they are the product of entangled states on adjacent sites. In each of these
states there is a non-zero staggered magnetization, which vanishes when we take
their translation-invariant combination as the new ground states. At the
Majumdar-Ghosh point, these entangled states become the spin-singlets
pertaining to this model. We will also calculate in closed form the two point
correlation functions, both for finite size of the chain and in the
thermodynamic limit.Comment: 11 page
New Phase Transitions in Optimal States for Memory Channels
We investigate the question of optimal input ensembles for memory channels
and construct a rather large class of Pauli channels with correlated noise
which can be studied analytically with regard to the entanglement of their
optimal input ensembles. In a more detailed study of a subclass of these
channels, the complete phase diagram of the two-qubit channel, which shows
three distinct phases is obtained. While increasing the correlation generally
changes the optimal state from separable to maximally entangled states, this is
done via an intermediate region where both separable and maximally entangled
states are optimal. A more concrete model, based on random rotations of the
error operators which mimic the behavior of this subclass of channels is also
presented.Comment: 13 pages, Late
Characterization of qutrit channels in terms of their covariance and symmetry properties
We characterize the completely positive trace-preserving maps on qutrits
(qutrit channels) according to their covariance and symmetry properties. Both
discrete and continuous groups are considered. It is shown how each symmetry
group restricts arbitrariness in the parameters of the channel to a very small
set. Although the explicit examples are related to qutrit channels, the
formalism is sufficiently general to be applied to qudit channels
Transition behavior in the capacity of correlated-noisy channels in arbitrary dimensions
We construct a class of quantum channels in arbitrary dimensions for which
entanglement improves the performance of the channel. The channels have
correlated noise and when the level of correlation passes a critical value we
see a sharp transition in the optimal input states (states which minimize the
output entropy) from separable to maximally entangled states. We show that for
a subclass of channels with some extra conditions, including the examples which
we consider, the states which minimize the output entropy are the ones which
maximize the mutual information.Comment: 11 pages, Latex, 4 figures, Accepted for publication in Physical
Review
Q-Boson Representation of the Quantum Matrix Algebra
{Although q-oscillators have been used extensively for realization of quantum
universal enveloping algebras,such realization do not exist for quantum matrix
algebras ( deformation of the algebra of functions on the group ). In this
paper we first construct an infinite dimensional representation of the quantum
matrix algebra (the coordinate ring of and then use
this representation to realize by q-bosons.}Comment: pages 18 ,report # 93-00
The matrix product representations for all valence bond states
We introduce a simple representation for irreducible spherical tensor
operators of the rotation group of arbitrary integer or half integer rank and
use these tensor operators to construct matrix product states corresponding to
all the variety of valence-bond states proposed in the
Affleck-Kennedy-Lieb-Tasaki (AKLT) construction. These include the fully
dimerized states of arbitrary spins, with uniform or alternating patterns of
spins, which are ground states of Hamiltonians with nearest and next-nearest
neighbor interactions, and the partially dimerized or AKLT/VBS (Valence Bond
Solid) states, which are constructed from them by projection. The latter states
are translation-invariant ground states of Hamiltonians with nearest-neighbor
interactions.Comment: 24 pages, references added, the version which appears in the journa
General Reaction-Diffusion Processes With Separable Equations for Correlation Functions
We consider general multi-species models of reaction diffusion processes and
obtain a set of constraints on the rates which give rise to closed systems of
equations for correlation functions. Our results are valid in any dimension and
on any type of lattice. We also show that under these conditions the evolution
equations for two point functions at different times are also closed. As an
example we introduce a class of two species models which may be useful for the
description of voting processes or the spreading of epidemics.Comment: 17 pages, Latex, No figure
Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation
A complete set of commuting observables for the Calogero-Gaudin system is
diagonalized, and the explicit form of the corresponding eigenvalues and
eigenfunctions is derived. We use a purely algebraic procedure exploiting the
co-algebra invariance of the model; with the proper technical modifications
this procedure can be applied to the deformed version of the model, which
is then also exactly solved.Comment: 20 pages Late
Photon losses depending on polarization mixedness
We introduce a quantum channel describing photon losses depending on the
degree of polarization mixedness. This can be regarded as a model of quantum
channel with correlated errors between discrete and continuous degrees of
freedom. We consider classical information over a continuous alphabet encoded
on weak coherent states as well as classical information over a discrete
alphabet encoded on single photons using dual rail representation. In both
cases we study the one-shot capacity of the channel and its behaviour in terms
of correlation between losses and polarization mixedness
An Exactly Solvable Two-Way Traffic Model With Ordered Sequential Update
Within the formalism of matrix product ansatz, we study a two-species
asymmetric exclusion process with backward and forward site-ordered sequential
update. This model, which was originally introduced with the random sequential
update, describes a two-way traffic flow with a dynamic impurity and shows a
phase transition between the free flow and traffic jam. We investigate the
characteristics of this jamming and examine similarities and differences
between our results and those with random sequential update.Comment: 25 pages, Revtex, 7 ps file
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