Related papers: Generalized quantum asymptotic equipartition
This paper defines, on the Galilean space-time, the group of asymptotically Euclidean transformations (AET), which are equivalent to Euclidean transformations at space-time infinity, and proposes a formulation of nonrelativistic quantum…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of special…
Given two pairs of quantum states, we want to decide if there exists a quantum channel that transforms one pair into the other. The theory of quantum statistical comparison and quantum relative majorization provides necessary and sufficient…
Impropriety testing for complex-valued vector has been considered lately due to potential applications ranging from digital communications to complex media imaging. This paper provides new results for such tests in the asymptotic regime,…
Distributed source simulation is the task where two (or more) parties share some correlated randomness and use local operations and no communication to convert this into some target correlation. Wyner's seminal result showed that…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…
We consider logics with truth values in the unit interval $[0,1]$. Such logics are used to define queries and to define probability distributions. In this context the notion of almost sure equivalence of formulas is generalized to the…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
The main topic of this thesis is the proof of two fundamental entropic inequalities for quantum Gaussian channels. Quantum Gaussian channels model the propagation of electromagnetic waves through optical fibers and free space in the quantum…
We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability…
In accordance with the entropy principle of thermodynamics, under spontaneous evolutions, physical systems always evolve towards states with equal or greater randomness. But, where does this randomness originate? Renowned Birkhoff-von…
Clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines. This paper develops an asymptotic theory for generalized estimating equations (GEE) analysis of clustered binary data…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model.…
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…
The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…