9,745 research outputs found

### Entropy inequalities from reflection positivity

We investigate the question of whether the entropy and the Renyi entropies of
the vacuum state reduced to a region of the space can be represented in terms
of correlators in quantum field theory. In this case, the positivity relations
for the correlators are mapped into inequalities for the entropies. We write
them using a real time version of reflection positivity, which can be
generalized to general quantum systems. Using this generalization we can prove
an infinite sequence of inequalities which are obeyed by the Renyi entropies of
integer index. There is one independent inequality involving any number of
different subsystems. In quantum field theory the inequalities acquire a simple
geometrical form and are consistent with the integer index Renyi entropies
being given by vacuum expectation values of twisting operators in the Euclidean
formulation. Several possible generalizations and specific examples are
analyzed.Comment: Significantly enlarged and corrected version. Counterexamples found
for the most general form of the inequalities. V3: minor change

### The logic of causally closed spacetime subsets

The causal structure of space-time offers a natural notion of an opposite or
orthogonal in the logical sense, where the opposite of a set is formed by all
points non time-like related with it. We show that for a general space-time the
algebra of subsets that arises from this negation operation is a complete
orthomodular lattice, and thus has several of the properties characterizing the
algebra physical propositions in quantum mechanics. We think this fact could be
used to investigate causal structure in an algebraic context. As a first step
in this direction we show that the causal lattice is in addition atomic, find
its atoms, and give necesary and sufficient conditions for ireducibility.Comment: 17 pages, 8 figure

### Mutual information challenges entropy bounds

We consider some formulations of the entropy bounds at the semiclassical
level. The entropy S(V) localized in a region V is divergent in quantum field
theory (QFT). Instead of it we focus on the mutual information
I(V,W)=S(V)+S(W)-S(V\cup W) between two different non-intersecting sets V and
W. This is a low energy quantity, independent of the regularization scheme. In
addition, the mutual information is bounded above by twice the entropy
corresponding to the sets involved. Calculations of I(V,W) in QFT show that the
entropy in empty space cannot be renormalized to zero, and must be actually
very large. We find that this entropy due to the vacuum fluctuations violates
the FMW bound in Minkowski space. The mutual information also gives a precise,
cutoff independent meaning to the statement that the number of degrees of
freedom increases with the volume in QFT. If the holographic bound holds, this
points to the essential non locality of the physical cutoff. Violations of the
Bousso bound would require conformal theories and large distances. We speculate
that the presence of a small cosmological constant might prevent such a
violation.Comment: 10 pages, 2 figures, minor change

### Remarks on the entanglement entropy for disconnected regions

Few facts are known about the entanglement entropy for disconnected regions
in quantum field theory. We study here the property of extensivity of the
mutual information, which holds for free massless fermions in two dimensions.
We uncover the structure of the entropy function in the extensive case, and
find an interesting connection with the renormalization group irreversibility.
The solution is a function on space-time regions which complies with all the
known requirements a relativistic entropy function has to satisfy. We show that
the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields
in dimensions greater than two, and the massive free fields in two dimensions
all fail to be exactly extensive, disproving recent conjectures.Comment: 14 pages, 4 figures, some addition

### Removal of Spectro-Polarimetric Fringes by 2D Pattern Recognition

We present a pattern-recognition based approach to the problem of removal of
polarized fringes from spectro-polarimetric data. We demonstrate that 2D
Principal Component Analysis can be trained on a given spectro-polarimetric map
in order to identify and isolate fringe structures from the spectra. This
allows us in principle to reconstruct the data without the fringe component,
providing an effective and clean solution to the problem. The results presented
in this paper point in the direction of revising the way that science and
calibration data should be planned for a typical spectro-polarimetric observing
run.Comment: ApJ, in pres

### An improved lion strategy for the lion and man problem

In this paper, a novel lion strategy for David Gale's lion and man problem is
proposed. The devised approach enhances a popular strategy proposed by Sgall,
which relies on the computation of a suitable "center". The key idea of the new
strategy is to update the center at each move, instead of computing it once and
for all at the beginning of the game. Convergence of the proposed lion strategy
is proven and an upper bound on the game length is derived, which dominates the
existing bounds.Comment: Preprint submitted to IEEE Control Systems Letter

### Continuous record Laplace-based inference about the break date in structural change models

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2018a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method.A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more preciseâ€”lower mean absolute error (MAE) and lower root-mean squared error (RMSE)â€”than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.First author draf

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