Related papers: Topological Aspects of Quantum Entanglement
Quantum characteristics of the Topological Non-connectivity Threshold (TNT), introduced in F.Borgonovi, G.L.Celardo, M.Maianti, E.Pedersoli, J. Stat. Phys., 116, 516 (2004), have been analyzed in the hard quantum regime. New interesting…
Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding…
We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-manifold in another.
We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of…
We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This…
Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have…
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…
The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained…
Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…
Non-locality or entanglement is an experimentally well established property of quantum mechanics. Here we study the role of quantum entanglement for higher symmetry group like $ SU(3_c) $, the gauge group of quantum chromodynamics (QCD). We…
Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing,…
We propose a new gauge theory of quantum electrodynamics (QED) and quantum chromodynamics (QCD) from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants…
In this paper we present a detailed study of \emph{bonded knots} and their related structures, integrating recent developments into a single framework. Bonded knots are classical knots endowed with embedded bonding arcs modeling physical or…
We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this…
We present here an overview of our work concerning entanglement properties of composite quantum systems. The characterization of entanglement, i.e. the possibility to assert if a given quantum state is entangled with others and how much…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
Although the homotopy-knot theory has been utilized to implement effective topological classification for non-Hermitian systems, the physical implications underlying distinct knot topologies remain ambiguous and are rarely addressed. In…
Quantum entanglement is a defining signature and resource of quantum theory, but its standard definition presupposes a globally fixed decomposition into subsystems. We develop a geometric framework that detects when such a decomposition…
Quantum entanglement -- correlations of particles that are stronger than any classical analogue -- is the basis for research on the foundations of quantum mechanics and for practical applications such as quantum networks. Traditionally,…
The standard, gapped entanglement boundary condition in Chern Simons theory breaks the topological invariance of the theory by introducing a complex structure on the entangling surface. This produces an infinite dimensional subregion…