相关论文: Strong Data Processing Inequalities and their Appl…
This essay explores strong data-processing inequalities (SPDI's) as they appear in the work of Evans and Schulman \cite{ES} and von Neumann \cite{vN} on computing with noisy circuits. We first develop the framework in \cite{ES}, which leads…
The data-processing inequality, that is, $I(U;Y) \le I(U;X)$ for a Markov chain $U \to X \to Y$, has been the method of choice for proving impossibility (converse) results in information theory and many other disciplines. Various…
The noisiness of a channel can be measured by comparing suitable functionals of the input and output distributions. For instance, the worst-case ratio of output relative entropy to input relative entropy for all possible pairs of input…
Strong data processing inequalities (SDPI) are an important object of study in Information Theory and have been well studied for $f$-divergences. Universal upper and lower bounds have been provided along with several applications,…
The data processing inequality (DPI) is a fundamental feature of information theory. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. When the smooth…
Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained.…
Let $\nu$ and $\mu$ be probability distributions on $\mathbb{R}^n$, and $\nu_s,\mu_s$ be their evolution under the heat flow, that is, the probability distributions resulting from convolving their density with the density of an isotropic…
Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized…
We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This approach is surprisingly powerful, and…
Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases. Numerical methods can handle arbitrary…
Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial…
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality…
This work provides data-processing and majorization inequalities for $f$-divergences, and it considers some of their applications to coding problems. This work also provides tight bounds on the R\'{e}nyi entropy of a function of a discrete…
We show that sharp thresholds for Boolean functions directly imply average-case circuit lower bounds. More formally we show that any Boolean function exhibiting a sharp enough threshold at \emph{arbitrary} critical density cannot be…
We study the fundamental problem of reliable interactive communication over a noisy channel. In a breakthrough sequence of papers published in 1992 and 1993, Schulman gave non-constructive proofs of the existence of general methods to…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
The paper is concerned with a dissipativity theory and robust performance analysis of discrete-time stochastic systems driven by a statistically uncertain random noise. The uncertainty is quantified by the conditional relative entropy of…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…