Related papers: Classification of sub-Cuntz states

We generalise the Kugo and Ojima formalism henceforth called KO) for the structure of state space in gauge theories, in four respects:- (i) We allow for a more general class of gauge-fixing including non-covariant cases. (ii) We display the…

Machine learning methods have been used to infer specific properties of limited families of optical quantum states, but a unified model that predicts a broad range of properties for practically relevant-especially multimode…

A new class of quantum states is introduced by demanding that the computational measurement statistics approach the Boltzmann distribution of higher-order strongly coupled Ising models. The states, referred to as $n$-coupled states, are…

A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3d). We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2N). This…

The diagram algebra introduced by Brauer that describes the centralizer algebra on tensor products of the natural representation of an orthogonal group has a presentation by generators and relations that only depends on the graph of type An…

Let $A$ be a separable simple exact ${\cal Z}$-stable $C^*$-algebra. We show that the unitay group of ${\tilde A}$ has the cancellation property. If $A$ has continuous scale, the Cuntz semigroup of $\tilde A$ has the strict comparison…

We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…

Lenz and Stollmann recently proved the existence of the integrated density of states in the sense of uniform convergence of the distributions for certain operators with aperiodic order. The goal of this paper is to establish a relation…

This paper provides an extensive study of the homotopy theory of types of algebras with units, like unital associative algebras or unital commutative algebras for instance. To this purpose, we endow the Koszul dual category of curved…

We offer the first operational interpretation of the $\alpha$-z relative entropies, a measure of distinguishability between two quantum states introduced by Jak\v{s}i\'c et al. and Audenaert and Datta. We show that these relative entropies…

We study the discrete state structure of $\hat c=1$ superconformal matter coupled to 2-D supergravity. Factorization properties of scattering amplitudes are used to identify these states and to construct the corresponding vertex operators.…

We classify a one-parameter family, $\mathfrak{confcarr}_z(d+1)$, of conformal extensions of the Carroll algebra in arbitrary dimension with $z$ being the anisotropic scaling exponent. We further obtain their infinite-dimensional…

We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low energy states. We identify multiple independent minimal entangled states, which…

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and…

Various generalizations of Cuntz algebras and their relations to symmetry and duality are reviewed. New generalized Cuntz algebras are associated with a subfactor. A characteristic Hilbert space of basic invariants (with respect to the…

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the…

We prove that a type II$_1$ factor $M$ can have at most one Cartan subalgebra $A$ satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class $\Cal H \Cal T$ of factors $M$…

We show that a tensor product among representation of certain C$^{*}$-algebras induces a bialgebra. Let $\tilde{{\cal O}}_{*}$ be the smallest unitization of the direct sum of Cuntz algebras \[{\cal O}_{*}\equiv {\bf C}\oplus {\cal…

Nonclassicality of quantum states is expressed in many shades, the most stringent of them being a new standard introduced recently in [Phys. Rev. A 89, 062110 (2014)]. This is accomplished by expanding the notion of local hidden variables…

This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$…