10,241 research outputs found
Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators
Let B=A+K where A is a bounded selfadjoint operator and K is an element of
the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an
enumeration of the discrete spectrum of B. We show that \sum_n
\dist(\lambda_n, \sigma(A))^p is bounded from above by a constant multiple of
|K|_p^p. We also derive a unitary analog of this estimate and apply it to
obtain new estimates on zero-sets of Cauchy transforms.Comment: Differences to previous version: Extended Introduction, new Section
5, additional references. To appear in Int. Eq. Op. Theor
Entanglement transformation with no classical communication
We present an optimal scheme to realize the transformations between single
copies of two bipartite entangled states without classical communication
between the sharing parties. The scheme achieves the upper bound for the
success probabilities [PRA 63, 022301 (2001), PRL 83, 1455 (1999)] of
generating maximally entangled states if applied to entanglement concentration.
Such strategy also dispenses with the interaction with an ancilla system in the
implementation. We also show that classical communications are indispensable in
realizing the deterministic transformations of a single bipartite entangled
state. With a finite number of identical pairs of two entangled bosons, on the
other hand, we can realize the deterministic transformation to any target
entangled state of equal or less Schmidt rank through an extension of the
scheme.Comment: published versio
Upper bounds on entangling rates of bipartite Hamiltonians
We discuss upper bounds on the rate at which unitary evolution governed by a
non-local Hamiltonian can generate entanglement in a bipartite system. Given a
bipartite Hamiltonian H coupling two finite dimensional particles A and B, the
entangling rate is shown to be upper bounded by c*log(d)*norm(H), where d is
the smallest dimension of the interacting particles, norm(H) is the operator
norm of H, and c is a constant close to 1. Under certain restrictions on the
initial state we prove analogous upper bound for the ancilla-assisted
entangling rate with a constant c that does not depend upon dimensions of local
ancillas. The restriction is that the initial state has at most two distinct
Schmidt coefficients (each coefficient may have arbitrarily large
multiplicity). Our proof is based on analysis of a mixing rate -- a functional
measuring how fast entropy can be produced if one mixes a time-independent
state with a state evolving unitarily.Comment: 14 pages, 4 figure
AR Sco as a possible seed of highly magnetised white dwarf
We explore the possibility that the recently discovered white dwarf pulsar AR
Sco acquired its high spin and magnetic field due to repeated episodes of
accretion and spin-down. An accreting white dwarf can lead to a larger mass and
consequently a smaller radius thus causing an enhanced rotation period and
magnetic field. This spinning magnetic white dwarf temporarily can inhibit
accretion, spin down, and, eventually, the accretion can start again due to the
shrinking of the binary period by gravitational radiation. A repeat of the
above cycle can eventually lead to a high magnetic field white dwarf, recently
postulated to be the reason for over-luminous type Ia supernovae. We also point
out that these high magnetic field spinning white dwarfs are attractive sites
for gravitational radiation.Comment: 7 pages including 4 figures; accepted for publication in MNRA
Taming computational complexity: efficient and parallel SimRank optimizations on undirected graphs
SimRank has been considered as one of the promising link-based ranking algorithms to evaluate similarities of web documents in many modern search engines. In this paper, we investigate the optimization problem of SimRank similarity computation on undirected web graphs. We first present a novel algorithm to estimate the SimRank between vertices in O(n3+ Kn2) time, where n is the number of vertices, and K is the number of iterations. In comparison, the most efficient implementation of SimRank algorithm in [1] takes O(K n3 ) time in the worst case. To efficiently handle large-scale computations, we also propose a parallel implementation of the SimRank algorithm on multiple processors. The experimental evaluations on both synthetic and real-life data sets demonstrate the better computational time and parallel efficiency of our proposed techniques
A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions
We study a matrix product state (MPS) algorithm to approximate excited states
of translationally invariant quantum spin systems with periodic boundary
conditions. By means of a momentum eigenstate ansatz generalizing the one of
\"Ostlund and Rommer [1], we separate the Hilbert space of the system into
subspaces with different momentum. This gives rise to a direct sum of effective
Hamiltonians, each one corresponding to a different momentum, and we determine
their spectrum by solving a generalized eigenvalue equation. Surprisingly, many
branches of the dispersion relation are approximated to a very good precision.
We benchmark the accuracy of the algorithm by comparison with the exact
solutions of the quantum Ising and the antiferromagnetic Heisenberg spin-1/2
model.Comment: 13 pages, 11 figures, 5 table
Time Optimal Control of Coupled Qubits Under Non-Stationary Interactions
In this article, we give a complete characterization of all the unitary
transformations that can be synthesized in a given time for a system of coupled
spin-1/2 in presence of general time varying coupling tensor. Our treatment is
quite general and our results help to characterize the reachable set at all
times for a class of bilinear control systems with time varying drift and
unbounded control amplitude. These results are of fundamental interest in
geometric control theory and have applications to control of coupled spins in
solid state NMR spectroscopy.Comment: 4 page
Constructing optimal entanglement witnesses. II
We provide a class of optimal nondecomposable entanglement witnesses for 4N x
4N composite quantum systems or, equivalently, a new construction of
nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This
construction provides natural generalization of the Robertson map. It is shown
that their structural physical approximations give rise to entanglement
breaking channels.Comment: 6 page
Convex Trace Functions on Quantum Channels and the Additivity Conjecture
We study a natural generalization of the additivity problem in quantum
information theory: given a pair of quantum channels, then what is the set of
convex trace functions that attain their maximum on unentangled inputs, if they
are applied to the corresponding output state?
We prove several results on the structure of the set of those convex
functions that are "additive" in this more general sense. In particular, we
show that all operator convex functions are additive for the Werner-Holevo
channel in 3x3 dimensions, which contains the well-known additivity results for
this channel as special cases.Comment: 9 pages, 1 figure. Published versio
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