Related papers: Differential geometry of density states
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…
We investigate the geometrical structure of multipartite states based on the construction of toric varieties. We show that the toric variety represents the space of general pure states and projective toric variety defines the space of…
We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In…
In quantum information theory, a geometric approach, known as "quantum information geometry," has been considered as a powerful method. In this thesis, we give a computational geometric interpretation to the geometric structure of a quantum…
The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is…
It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
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…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to 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…
The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY.…
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
This is a report on recent progress concerning the interactions between derived algebraic geometry and deformation quantization. We present the notion of derived algebraic stacks, of shifted symplectic and Poisson structures, as well as the…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…
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…