Related papers: Symplectic geometry of entanglement
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
We introduce an experimental procedure for the detection of quantum entanglement of an unknown quantum state with as few measurements as possible. The method requires neither a priori knowledge of the state nor a shared reference frame…
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
We attempt to reveal the geometry, emerged from the entanglement structure of any general $N$-party pure quantum many-body state by representing entanglement entropies corresponding to all $2^N $ bipartitions of the state by means of a…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction.…
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single…
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states…
We generalize the symmetric multi-qubit states to their q-analogs, whose basis vectors are identified with the q-Dicke states. We study the entanglement entropy in these states and find that entanglement is extruded towards certain regions…
We describe the action of the symplectic group on the homogeneous space of squeezed states (quantum blobs) and extend this action to the semigroup. We then extend the metaplectic representation to the metaplectic (or oscillator) semigroup…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
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…
Entanglement asymmetry is an observable in quantum systems, constructed using quantum-information methods, suited to detecting symmetry breaking in states -- possibly out of equilibrium -- relative to a subsystem. In this paper we define…
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…
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 quantum homology of the monotone complex quadric surface splits into the sum of two fields. We outline a proof of the following statement: The unities of these fields give rise to distinct symplectic quasi-states defined by asymptotic…
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into…
Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view…
The main objective of the paper is to unveil an adequate mathematics hidden behind entanglement, that is Geometric Invariant Theory. More specifically relation between these two subjects can be described by the following theses. (i) Total…