55 research outputs found
Key Capacity with Limited One-Way Communication for Product Sources
We show that for product sources, rate splitting is optimal for secret key
agreement using limited one-way communication at two terminals. This yields an
alternative proof of the tensorization property of a strong data processing
inequality originally studied by Erkip and Cover and amended recently by
Anantharam et al. We derive a `water-filling' solution of the
communication-rate--key-rate tradeoff for two arbitrarily correlated vector
Gaussian sources, for the case with an eavesdropper, and for stationary
Gaussian processes.Comment: 5 pages, ISIT 201
Maximal Entanglement - A New Measure of Entanglement
Maximal correlation is a measure of correlation for bipartite distributions.
This measure has two intriguing features: (1) it is monotone under local
stochastic maps; (2) it gives the same number when computed on i.i.d. copies of
a pair of random variables. This measure of correlation has recently been
generalized for bipartite quantum states, for which the same properties have
been proved. In this paper, based on maximal correlation, we define a new
measure of entanglement which we call maximal entanglement. We show that this
measure of entanglement is faithful (is zero on separable states and positive
on entangled states), is monotone under local quantum operations, and gives the
same number when computed on tensor powers of a bipartite state.Comment: 8 pages, presented at IWCIT 201
Brascamp-Lieb Inequality and Its Reverse: An Information Theoretic View
We generalize a result by Carlen and Cordero-Erausquin on the equivalence
between the Brascamp-Lieb inequality and the subadditivity of relative entropy
by allowing for random transformations (a broadcast channel). This leads to a
unified perspective on several functional inequalities that have been gaining
popularity in the context of proving impossibility results. We demonstrate that
the information theoretic dual of the Brascamp-Lieb inequality is a convenient
setting for proving properties such as data processing, tensorization,
convexity and Gaussian optimality. Consequences of the latter include an
extension of the Brascamp-Lieb inequality allowing for Gaussian random
transformations, the determination of the multivariate Wyner common information
for Gaussian sources, and a multivariate version of Nelson's hypercontractivity
theorem. Finally we present an information theoretic characterization of a
reverse Brascamp-Lieb inequality involving a random transformation (a multiple
access channel).Comment: 5 pages; to be presented at ISIT 201
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