668 research outputs found
Solving Variational Inequalities Defined on A Domain with Infinitely Many Linear Constraints
We study a variational inequality problem whose domain
is defined by infinitely many linear inequalities. A
discretization method and an analytic center based
inexact cutting plane method are proposed. Under proper
assumptions, the convergence results for both methods are
given. We also provide numerical examples for the
proposed methods
Better Bell Inequality Violation by Collective Measurements
The standard Bell inequality experiments test for violation of local realism
by repeatedly making local measurements on individual copies of an entangled
quantum state. Here we investigate the possibility of increasing the violation
of a Bell inequality by making collective measurements. We show that
nonlocality of bipartite pure entangled states, quantified by their maximal
violation of the Bell-Clauser-Horne inequality, can always be enhanced by
collective measurements, even without communication between the parties. For
mixed states we also show that collective measurements can increase the
violation of Bell inequalities, although numerical evidence suggests that the
phenomenon is not common as it is for pure states.Comment: 7 pages, 4 figures and 1 table; references update
Symmetry analysis of crystalline spin textures in dipolar spinor condensates
We study periodic crystalline spin textures in spinor condensates with
dipolar interactions via a systematic symmetry analysis of the low-energy
effective theory. By considering symmetry operations which combine real and
spin space operations, we classify symmetry groups consistent with non-trivial
experimental and theoretical constraints. Minimizing the energy within each
symmetry class allows us to explore possible ground states.Comment: 19 pages, 4 figure
Semi-device-independent bounds on entanglement
Detection and quantification of entanglement in quantum resources are two key
steps in the implementation of various quantum-information processing tasks.
Here, we show that Bell-type inequalities are not only useful in verifying the
presence of entanglement but can also be used to bound the entanglement of the
underlying physical system. Our main tool consists of a family of
Clauser-Horne-like Bell inequalities that cannot be violated maximally by any
finite-dimensional maximally entangled state. Using these inequalities, we
demonstrate the explicit construction of both lower and upper bounds on the
concurrence for two-qubit states. The fact that these bounds arise from
Bell-type inequalities also allows them to be obtained in a
semi-device-independent manner, that is, with assumption of the dimension of
the Hilbert space but without resorting to any knowledge of the actual
measurements being performed on the individual subsystems.Comment: 8 pages, 2 figures (published version). Note 1: Title changed to
distinguish our approach from the standard device-independent scenario where
no assumption on the Hilbert space dimension is made. Note 2: This paper
contains explicit examples of more nonlocality with less entanglement in the
simplest CH-like scenario (see also arXiv:1011.5206 by Vidick and Wehner for
related results
Entropic Regularization Approach for Mathematical Programs with Equilibrium Constraints
A new smoothing approach based on entropic perturbation
is proposed for solving mathematical programs with
equilibrium constraints. Some of the desirable
properties of the smoothing function are shown. The
viability of the proposed approach is supported by a
computationalstudy on a set of well-known test problems
Bounds on Quantum Correlations in Bell Inequality Experiments
Bell inequality violation is one of the most widely known manifestations of
entanglement in quantum mechanics; indicating that experiments on physically
separated quantum mechanical systems cannot be given a local realistic
description. However, despite the importance of Bell inequalities, it is not
known in general how to determine whether a given entangled state will violate
a Bell inequality. This is because one can choose to make many different
measurements on a quantum system to test any given Bell inequality and the
optimization over measurements is a high-dimensional variational problem. In
order to better understand this problem we present algorithms that provide, for
a given quantum state, both a lower bound and an upper bound on the maximal
expectation value of a Bell operator. Both bounds apply techniques from convex
optimization and the methodology for creating upper bounds allows them to be
systematically improved. In many cases these bounds determine measurements that
would demonstrate violation of the Bell inequality or provide a bound that
rules out the possibility of a violation. Examples are given to illustrate how
these algorithms can be used to conclude definitively if some quantum states
violate a given Bell inequality.Comment: 13 pages, 1 table, 2 figures. Updated version as published in PR
On the Finite Termination of An Entropy Function Based Smoothing Newton Method for Vertical Linear Complementarity Problems
By using a smooth entropy function to approximate the non-smooth max-type function, a vertical
linear complementarity problem (VLCP) can be treated as a family of parameterized smooth
equations. A Newton-type method with a testing procedure is proposed to solve such
a system. We show that the proposed algorithm finds an exact solution of VLCP in a finite
number of iterations, under some conditions milder than those assumed in literature. Some
computational results are included to illustrate the potential of this approach
Recursive Approximation of the High Dimensional max Function
An alternative smoothing method for the high dimensional max function
has been studied. The proposed method is a recursive extension of the
two dimensional smoothing functions. In order to analyze the proposed
method, a theoretical framework related to smoothing methods has been
discussed. Moreover, we support our discussion by considering some
application areas. This is followed by a comparison with an
alternative well-known smoothing method
Bell inequalities for three systems and arbitrarily many measurement outcomes
We present a family of Bell inequalities for three parties and arbitrarily
many outcomes, which can be seen as a natural generalization of the Mermin Bell
inequality. For a small number of outcomes, we verify that our inequalities
define facets of the polytope of local correlations. We investigate the quantum
violations of these inequalities, in particular with respect to the Hilbert
space dimension. We provide strong evidence that the maximal quantum violation
can only be reached using systems with local Hilbert space dimension exceeding
the number of measurement outcomes. This suggests that our inequalities can be
used as multipartite dimension witnesses.Comment: v1 6 pages, 4 tables; v2 Published version with minor typos correcte
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