Related papers: Geometric and Information-Theoretic Properties of …
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…
Quantum descriptions of many complex systems are formulated most naturally in bases of states that are not mutually orthogonal. We introduce a general and powerful yet simple approach that facilitates solving such models exactly by…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
In the present study we revisit the application of the $q$-information measures $R_q$ of R\'enyi's and $S_q$ of Tsallis' to the discussion of special features of two qubits systems. More specifically, we study the correlations between the…
The aim of the present paper is twofold. First, to give the main ideas behind quantum computingand quantum information, a field based on quantum-mechanical phenomena. Therefore, a shortreview is devoted to (i) quantum bits or qubits (and…
We start with the simplest quantum system (a two-level system, i.e., a qubit) and discuss a one-to-one mapping of the quantum state in a two-dimensional Hilbert space to a vector in an eight dimensional probability space (probability…
We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon…
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination,…
In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
Quantum engineering now allows to design and construct multi-qubit states in a range of physical systems. These states are typically quite complex in nature, with disparate, but relevant properties that include both single and multi-qubit…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal…
Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the…
Based on the geometry of entangled three and two qubit states, we present the connection between the entanglement measure of the three-qubit state defined using the last Hopf fibration and the entanglement measures known as two- and…
We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…