Related papers: Partially smoothed information measures
Given an arbitrary measurement over a system of interest, the outcome of a posterior measurement can be used for improving the statistical estimation of the system state after the former measurement. Here, we realize an…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…
One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence and information spectrum divergence, that characterize various operational tasks and are used to…
Recently, Anshu et al. introduced "partially" smoothed information measures and used them to derive tighter bounds for several information-processing tasks, including quantum state merging and privacy amplification against quantum…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
We study formal properties of smooth max-information, a generalization of von Neumann mutual information derived from the max-relative entropy. Recent work suggests that it is a useful quantity in one-shot channel coding, quantum rate…
Partially smoothed information measures are fundamental tools in one-shot quantum information theory. In this work, we determine the exact strong converse exponents of these measures for both pure quantum states and classical states.…
Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from future measurements (smoothing). While classical smoothing is…
Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both past and future) observations. Here we define a smoothed quantum state for a…
We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic…
Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal ({\em i.e.}referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
Smoothing is a technique for estimating the state of an imperfectly monitored open system by combining both prior and posterior measurement information. In the quantum regime, current approaches to smoothing either give unphysical outcomes,…
We propose a general measure of non-classical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure…
The fidelity-based smooth min-relative entropy is a distinguishability measure that has appeared in a variety of contexts in prior work on quantum information, including resource theories like thermodynamics and coherence. Here we provide a…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
Quantum information theory and quantum computing are theoritical basis of quantum computers. Thanks to entanglement, quantum mechanical systems are provisioned to realize many information processing problems faster than classical…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…