Related papers: States on EMV-algebras
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
Statistical mechanics for states with complex eigenvalues, which are described by Gel'fand triplet and represent unstable states like resonances, are discussed on the basis of principle of equal ${\it a priori}$ probability. A new entropy…
The notion of commutativity of two normal states on a von Neumann algebra was defined some time ago by means of the Pedersen-Takesaki theorem. In this note we aim at generalizing this notion to an arbitrary number of states, and obtaining…
We generalize the Majorana stellar representation of spin-$s$ pure states to mixed states, and in general to any hermitian operator, defining a bijective correspondence between three spaces: the spin density-matrices, a projective space of…
State monads in cartesian closed categories are those defined by the familiar adjunction between product and exponential. We investigate the structure of their algebras, and show that the exponential functor is monadic provided the base…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct…
The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purification map), which is nonlinear map, is introduced. The density…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
We prove the existence of the V-states for the generalized inviscid SQG equations with $\alpha\in ]0,1[.$ These structures are special rotating simply connected patches with $m-$ fold symmetry bifurcating from the trivial solution at some…
Computing the entanglement of formation of a bipartite state is generally difficult, but special symmetries of a state can simplify the problem. For instance, this allows one to determine the entanglement of formation of Werner states and…
We present an algebraic theory of the states of the infinite classical lattices. The construction follows the Haag-Kastler axioms from quantum field theory. By comparison, the *-algebras of the quantum theory are replaced here with the…
Complex techniques of general relativity are used to determine \emph{all} the states in the two and three dimensional momentum spaces in which the equality holds in the uncertainty relations for the non-commuting basic observables of…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
Relations between states and maps, which are known for quantum systems in finite-dimensional Hilbert spaces, are formulated rigorously in geometrical terms with no use of coordinate (matrix) interpretation. In a tensor product realization…
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
In this Thesis we will explicitly construct Hadamard states with different features. In the two first cases, the states will be constructed in static and in cosmological spacetimes. In one of the cases, the states will be constructed in…
For Hilbert spaces $\mathcal H\subseteq L^2(\mathbb R)$ we consider the convex sets $\mathcal D_+(\mathcal H)$ of Wigner-positive states (WPS), i.e.~density matrices over $\mathcal H$ with non-negative Wigner function. We investigate the…