Related papers: A geometric framework for mixed quantum states bas…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
We present a construction of genuinely entangled multipartite quantum states based on the group theory. Analyzed states resemble the Dicke states, whereas the interactions occur only between specific subsystems related by the action of the…
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are…
This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…
Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive…
In this paper we study the geometrical structures of multi-qubit states based on symplectic toric manifolds. After a short review of symplectic toric manifolds, we discuss the space of a single quantum state in terms of these manifolds. We…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
Coherent states for a general Lie superalgebra are defined following the method originally proposed by Perelomov. Algebraic and geometrical properties of the systems of states thus obtained are examined, with particular attention to the…
The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered…
It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…
We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the…
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…
It has been often observed that K\"ahler geometry is essentially a $U(1)$ gauge theory whose field strength is identified with the K\"ahler form. However it has been pursued neither seriously nor deeply. We argue that this remarkable…
While several measures exist for entanglement of multipartite pure states, a true entanglement measure for mixed states still eludes us. A deeper study of the geometry of quantum states may be the way to address this issue, on which context…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold…