7,698 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
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
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
Optimal universal programmable detectors for unambiguous discrimination
We discuss the problem of designing unambiguous programmable discriminators
for any n unknown quantum states in an m-dimensional Hilbert space. The
discriminator is a fixed measurement that has two kinds of input registers: the
program registers and the data register. The quantum state in the data register
is what users want to identify, which is confirmed to be among the n states in
program registers. The task of the discriminator is to tell the users which
state stored in the program registers is equivalent to that in the data
register. First, we give a necessary and sufficient condition for judging an
unambiguous programmable discriminator. Then, if , we present an optimal
unambiguous programmable discriminator for them, in the sense of maximizing the
worst-case probability of success. Finally, we propose a universal unambiguous
programmable discriminator for arbitrary n quantum states.Comment: 7 page
Quantum correlations and least disturbing local measurements
We examine the evaluation of the minimum information loss due to an unread
local measurement in mixed states of bipartite systems, for a general entropic
form. Such quantity provides a measure of quantum correlations, reducing for
pure states to the generalized entanglement entropy, while in the case of mixed
states it vanishes just for classically correlated states with respect to the
measured system, as the quantum discord. General stationary conditions are
provided, together with their explicit form for general two-qubit states.
Closed expressions for the minimum information loss as measured by quadratic
and cubic entropies are also derived for general states of two-qubit systems.
As application, we analyze the case of states with maximally mixed marginals,
where a general evaluation is provided, as well as X states and the mixture of
two aligned states.Comment: 10 pages, 3 figure
Quantum Correlations in Large-Dimensional States of High Symmetry
In this article, we investigate how quantum correlations behave for the
so-called Werner and pseudo-pure families of states. The latter refers to
states formed by mixing any pure state with the totally mixed state. We derive
closed expressions for the Quantum Discord (QD) and the Relative Entropy of
Quantumness (REQ) for these families of states. For Werner states, the
classical correlations are seen to vanish in high dimensions while the amount
of quantum correlations remain bounded and become independent of whether or not
the the state is entangled. For pseudo-pure states, nearly the opposite effect
is observed with both the quantum and classical correlations growing without
bound as the dimension increases and only as the system becomes more entangled.
Finally, we verify that pseudo-pure states satisfy the conjecture of
[\textit{Phys. Rev. A} \textbf{84}, 052110 (2011)] which says that the
Geometric Measure of Discord (GD) always upper bounds the squared Negativity of
the state
Determination of maximal Gaussian entanglement achievable by feedback-controlled dynamics
We determine a general upper bound for the steady-state entanglement
achievable by continuous feedback for systems of any number of bosonic degrees
of freedom. We apply such a bound to the specific case of parametric
interactions - the most common practical way to generate entanglement in
quantum optics - and single out optimal feedback strategies that achieve the
maximal entanglement. We also consider the case of feedback schemes entirely
restricted to local operations and compare their performance to the optimal,
generally nonlocal, schemes.Comment: 4 pages. Published versio
Quadratic Dynamical Decoupling with Non-Uniform Error Suppression
We analyze numerically the performance of the near-optimal quadratic
dynamical decoupling (QDD) single-qubit decoherence errors suppression method
[J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is
formed by nesting two optimal Uhrig dynamical decoupling sequences for two
orthogonal axes, comprising N1 and N2 pulses, respectively. Varying these
numbers, we study the decoherence suppression properties of QDD directly by
isolating the errors associated with each system basis operator present in the
system-bath interaction Hamiltonian. Each individual error scales with the
lowest order of the Dyson series, therefore immediately yielding the order of
decoherence suppression. We show that the error suppression properties of QDD
are dependent upon the parities of N1 and N2, and near-optimal performance is
achieved for general single-qubit interactions when N1=N2.Comment: 17 pages, 22 figure
Extremal extensions of entanglement witnesses: Unearthing new bound entangled states
In this paper, we discuss extremal extensions of entanglement witnesses based
on Choi's map. The constructions are based on a generalization of the Choi map
due to Osaka, from which we construct entanglement witnesses. These extremal
extensions are powerful in terms of their capacity to detect entanglement of
positive under partial transpose (PPT) entangled states and lead to unearthing
of entanglement of new PPT states. We also use the Cholesky-like decomposition
to construct entangled states which are revealed by these extremal entanglement
witnesses.Comment: 8 pages 6 figures revtex4-
Entanglement of pure states for a single copy
An optimal local conversion strategy between any two pure states of a
bipartite system is presented. It is optimal in that the probability of success
is the largest achievable if the parties which share the system, and which can
communicate classically, are only allowed to act locally on it. The study of
optimal local conversions sheds some light on the entanglement of a single copy
of a pure state. We propose a quantification of such an entanglement by means
of a finite minimal set of new measures from which the optimal probability of
conversion follows.Comment: Revtex, 4 pages, no figures. Minor changes. Appendix remove
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