Related papers: Quantum Knots and Mosaics
A knot is a circle embedded in the space. Projecting a knot on a plane, we obtain a diagram which is known as the knot diagram. The vertices of the diagram, where the curved lines are crossed, can be considered as sites occupied by…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
This paper treats a quantum network from a physical approach, explicitly finds the physical eigenstates and compares them to the quantum-graph description. The basic building block of a quantum network is an X-shaped potential well made by…
We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
The open-system dynamics of entanglement plays an important role in the assessment of the robustness of quantum information processes and also in the investigation of the classical limit of quantum mechanics. Here we show that, subjacent to…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
Packaged quantum states are gauge-invariant states in which all internal quantum numbers (IQNs) form an inseparable block. This feature gives rise to novel packaged entanglements that encompass all IQNs, which is important both for…
Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or…
The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture.…
This article is an introduction to quant-ph/0302092. We propose to quantify how "quantum" a set of quantum states is. The quantumness of a set is the worst-case difficulty of transmitting the states through a classical communication…
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\cal A$ of operationally relevant observables. The algebraic structure of $\cal A$ selects a preferred tensor product…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
The state $\rho$ of a quantum system can be represented by a vector $\mathbf{P}_{\mathcal{M}}(\rho)$ of outcome probabilities for a set of measurements $\mathcal{M}$. Such representations appear throughout physics, for example, in quantum…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
We discuss maximum entangled states of quantum systems in terms of quantum fluctuations of all essential measurements responsible for manifestation of entanglement. Namely, we consider maximum entanglement as a property of states, for which…
We introduce the notion of quantum computational webs: These are quantum states universal for measurement-based computation which can be built up from a collection of simple primitives. The primitive elements - reminiscent of building…