Related papers: Extensions of the quantum Fano inequality
We study the fully entangled fraction (FEF) of arbitrary mixed states. New upper bounds of FEF are derived. These upper bounds make complements on the estimation of the value of FEF. For weakly mixed quantum states, an upper bound is shown…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Entanglement R\'enyi-$\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement R\'enyi-$\alpha$…
We discuss the generalized von Neumann (Tsallis) entropy and the generalized Fisher information (GFI) in nonextensive quantum systems, by using the interpolation approximation (IA) which has been shown to yield good results for the quantal…
We replace a Hamiltonian with a modular Hamiltonian in the spectral form factor and the level spacing distribution function. This study establishes a connection between quantities within Quantum Entanglement and Quantum Chaos. To have a…
Deriving formulations for computing and estimating tight worst-case size increases for conjunctive queries with various constraints has been at the core of theoretical database research. If the problem has no constraints or only one…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…
Research in quantum information science aims to surpass the scaling limitations of classical information processing. From a physicist's perspective, performance improvement involves a physical speedup in the quantum domain, achieved by…
Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in any non-contextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of…
We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite…
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…
We study the fundamental properties of the quantum f-relative entropy, where f(.) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they…
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
The entanglement fidelity provides a measure of how well the entanglement between two subsystems is preserved in a quantum process. By using a simple model we show that in some cases this quantity in its original definition fails in the…
The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of…
We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…