Notes on Information-Theoretic Privacy

We investigate the tradeoff between privacy and utility in a situation where both privacy and utility are measured in terms of mutual information. For the binary case, we fully characterize this tradeoff in case of perfect privacy and also give an upper-bound for the case where some privacy leakage is allowed. We then introduce a new quantity which quantifies the amount of private information contained in the observable data and then connect it to the optimal tradeoff between privacy and utility.Comment: The corrected version of a paper appeared in Allerton 201

Privacy-Aware MMSE Estimation

We investigate the problem of the predictability of random variable $Y$ under a privacy constraint dictated by random variable $X$, correlated with $Y$, where both predictability and privacy are assessed in terms of the minimum mean-squared error (MMSE). Given that $X$ and $Y$ are connected via a binary-input symmetric-output (BISO) channel, we derive the \emph{optimal} random mapping $P_{Z|Y}$ such that the MMSE of $Y$ given $Z$ is minimized while the MMSE of $X$ given $Z$ is greater than $(1-\epsilon)\mathsf{var}(X)$ for a given $\epsilon\geq 0$. We also consider the case where $(X,Y)$ are continuous and $P_{Z|Y}$ is restricted to be an additive noise channel.Comment: 9 pages, 3 figure

Higgs pair production in vector-boson fusion at the LHC and beyond

The production of pairs of Higgs bosons at hadron colliders provides unique information on the Higgs sector and on the mechanism underlying electroweak symmetry breaking (EWSB). Most studies have concentrated on the gluon fusion production mode which has the largest cross section. However, despite its small production rate, the vector-boson fusion channel can also be relevant since even small modifications of the Higgs couplings to vector bosons induce a striking increase of the cross section as a function of the invariant mass of the Higgs boson pair. In this work, we exploit this unique signature to propose a strategy to extract the $hhVV$ quartic coupling and provide model-independent constraints on theories where EWSB is driven by new strong interactions. We take advantage of the higher signal yield of the $b\bar b b\bar b$ final state and make extensive use of jet substructure techniques to reconstruct signal events with a boosted topology, characteristic of large partonic energies, where each Higgs boson decays to a single collimated jet . Our results demonstrate that the $hhVV$ coupling can be measured with 45% (20%) precision at the LHC for $\mathcal{L}=$ 300 (3000) fb$^{-1}$, while a 1% precision can be achieved at a 100 TeV collider.Comment: Updated to match published version in EPJC and fixed typo in Tab. 10 (column labels a & b were swapped