Related papers: Symplectic Structures in Quantum Entanglement
A new framework is formulated to study entanglement dynamics in many-body quantum systems along with an associated geometric description. In this formulation, called the Quantum Correlation Transfer Function (QCTF), the system's wave…
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,…
New inequalities for symplectic tomograms of quantum states and their connection with entropic uncertainty relations are discussed within the framework of the probability representation of quantum mechanics.
We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric…
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…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
By investigating the symplectic geometry and geometric quantization on a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed and q-deformed cases in the classical as well as in the…
The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (see Shimony 1995 and…
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…
The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes…
When a quantum pure state is drawn uniformly at random from a Hilbert space, the state is typically highly entangled. This property of a random state is known as generic entanglement of quantum states and has been long investigated from…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…