3,124 research outputs found
Purification-based metric to measure the distance between quantum states and processes
In this work we study the properties of an purification-based entropic metric
for measuring the distance between both quantum states and quantum processes.
This metric is defined as the square root of the entropy of the average of two
purifications of mixed quantum states which maximize the overlap between the
purified states. We analyze this metric and show that it satisfies many
appealing properties, which suggest this metric is an interesting proposal for
theoretical and experimental applications of quantum information.Comment: 11 pages, 2 figures. arXiv admin note: text overlap with
arXiv:quant-ph/0408063, arXiv:1107.1732 by other author
Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems
We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the bi-harmonic operator with those intermediate boundary conditions which ap-pears in the study of hinged plates. In this case, we analyze the spectral behavior when the boundary of the domain is subject to a periodic oscillatory perturbation. We will show that there is a critical oscillatory behavior and the limit problem depends on whether we are above, below or just sitting on this critical value. In particular, in the critical case we identify the strange term appearing in the limiting boundary conditions by using the unfolding method from homogenization theory
A family of generalized quantum entropies: definition and properties
We present a quantum version of the generalized -entropies,
introduced by Salicr\'u \textit{et al.} for the study of classical probability
distributions. We establish their basic properties, and show that already known
quantum entropies such as von Neumann, and quantum versions of R\'enyi,
Tsallis, and unified entropies, constitute particular classes of the present
general quantum Salicr\'u form. We exhibit that majorization plays a key role
in explaining most of their common features. We give a characterization of the
quantum -entropies under the action of quantum operations, and study
their properties for composite systems. We apply these generalized entropies to
the problem of detection of quantum entanglement, and introduce a discussion on
possible generalized conditional entropies as well.Comment: 26 pages, 1 figure. Close to published versio
Unified entropic measures of quantum correlations induced by local measurements
We introduce quantum correlations measures based on the minimal change in
unified entropies induced by local rank-one projective measurements, divided by
a factor that depends on the generalized purity of the system in the case of
non-additive entropies. In this way, we overcome the issue of the artificial
increasing of the value of quantum correlations measures based on non-additive
entropies when an uncorrelated ancilla is appended to the system without
changing the computability of our entropic correlations measures with respect
to the previous ones. Moreover, we recover as limiting cases the quantum
correlations measures based on von Neumann and R\'enyi entropies (i.e.,
additive entropies), for which the adjustment factor becomes trivial. In
addition, we distinguish between total and semiquantum correlations and obtain
some relations between them. Finally, we obtain analytical expressions of the
entropic correlations measures for typical quantum bipartite systems.Comment: 10 pages, 1 figur
Jensen Shannon divergence as a measure of the degree of entanglement
The notion of distance in Hilbert space is relevant in many scenarios. In
particular, distances between quantum states play a central role in quantum
information theory. An appropriate measure of distance is the quantum Jensen
Shannon divergence (QJSD) between quantum states. Here we study this distance
as a geometrical measure of entanglement and apply it to different families of
states.Comment: 5 pages, 2 figures, to appear in the special issue of IJQI "Noise,
Information and Complexity at Quantum Scale", eds. S. Mancini and F.
Marcheson
Natural Metric for Quantum Information Theory
We study in detail a very natural metric for quantum states. This new
proposal has two basic ingredients: entropy and purification. The metric for
two mixed states is defined as the square root of the entropy of the average of
representative purifications of those states. Some basic properties are
analyzed and its relation with other distances is investigated. As an
illustrative application, the proposed metric is evaluated for 1-qubit mixed
states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto
Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues
We consider the Steklov eigenvalues of the Laplace operator as limiting
Neumann eigenvalues in a problem of boundary mass concentration. We discuss the
asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the
Steklov eigenvalues minimize the Neumann eigenvalues. Moreover, we study the
dependence of the eigenvalues of the Steklov problem upon perturbation of the
mass density and show that the Steklov eigenvalues violates a maximum principle
in spectral optimization problems.Comment: This is a preprint version of a paper that will appear in the
Proceedings of the 9th ISAAC Congress, Krak\'ow 201
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