Related papers: Monotones from multi-invariants: a classification
In this paper we describe a method for finding polynomial invariants under Stochastic Local Operations and Classical Communication (SLOCC), for a system of delocalized fermions shared between different parties, with global particle number…
Various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability and behavior under measurement are looked…
We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalizes existing criteria. Each condition corresponds to a convex optimization…
We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
Modern applications of algebraic topology to point cloud data analysis have motivated active investigation of combinatorial clique complexes -- high-dimensional extensions of combinatorial graphs. We show that meaningful invariants of such…
Classical spectral graph theory characterizes graphs with logarithmic mixing time. In this work, we present a combinatorial characterization of graphs with constant mixing time. The combinatorial characterization is based on the small-set…
The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. We distinguish an open dense subset of the real big cone, called the stable…
Bott--Cattaneo's theory defines the integral invariants for a framed rational homology 3-sphere equipped with an acyclic orthogonal local system, in terms of graph cocycles without self-loops. The 2-loop term of their invariants is…
Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear…
The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I_5 of pure three-qubit states. It is found to being an independent invariant only in presence of both…
This is a short survey on idempotent states on locally compact groups and locally compact quantum groups. The central topic is the relationship between idempotent states, subgroups and invariant C*-subalgebras. We concentrate on recent…
We study the multivariate independence polynomials of graphs and the log-concavity of the coefficients of their univariate restrictions. Let $R_{W_4}$ be the operator defined on simple and undirected graphs which replaces each edge with a…
In this article, we introduce rack invariants of oriented Legendrian knots in the 3-dimensional Euclidean space endowed with the standard contact structure, which we call Legendrian racks. These invariants form a generalization of the…
We explore a geometric approach to generating local SU(2) and $SL(2,\mathbb{C})$ invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or 'gauge' invariant is associated to a distinct closed path (or…
We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically…
In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions…
We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…
We give a one-to-one correspondence between classes of density matrices under local unitary invariance and the double cosets of unitary groups. We show that the interrelationship among classes of local unitary equivalent multi-partite mixed…