3,817 research outputs found
On the lattice structure of probability spaces in quantum mechanics
Let C be the set of all possible quantum states. We study the convex subsets
of C with attention focused on the lattice theoretical structure of these
convex subsets and, as a result, find a framework capable of unifying several
aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent
principle. We also encounter links with entanglement witnesses, which leads to
a new separability criteria expressed in lattice language. We also provide an
extension of a separability criteria based on convex polytopes to the infinite
dimensional case and show that it reveals interesting facets concerning the
geometrical structure of the convex subsets. It is seen that the above
mentioned framework is also capable of generalization to any statistical theory
via the so-called convex operational models' approach. In particular, we show
how to extend the geometrical structure underlying entanglement to any
statistical model, an extension which may be useful for studying correlations
in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416
Bayesian linear inverse problems in regularity scales
We obtain rates of contraction of posterior distributions in inverse problems
defined by scales of smoothness classes. We derive abstract results for general
priors, with contraction rates determined by Galerkin approximation. The rate
depends on the amount of prior concentration near the true function and the
prior mass of functions with inferior Galerkin approximation. We apply the
general result to non-conjugate series priors, showing that these priors give
near optimal and adaptive recovery in some generality, Gaussian priors, and
mixtures of Gaussian priors, where the latter are also shown to be near optimal
and adaptive. The proofs are based on general testing and approximation
arguments, without explicit calculations on the posterior distribution. We are
thus not restricted to priors based on the singular value decomposition of the
operator. We illustrate the results with examples of inverse problems resulting
from differential equations.Comment: 34 page
The role of quantum information in thermodynamics --- a topical review
This topical review article gives an overview of the interplay between
quantum information theory and thermodynamics of quantum systems. We focus on
several trending topics including the foundations of statistical mechanics,
resource theories, entanglement in thermodynamic settings, fluctuation theorems
and thermal machines. This is not a comprehensive review of the diverse field
of quantum thermodynamics; rather, it is a convenient entry point for the
thermo-curious information theorist. Furthermore this review should facilitate
the unification and understanding of different interdisciplinary approaches
emerging in research groups around the world.Comment: published version. 34 pages, 6 figure
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