Related papers: Differential geometry of density states
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
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…
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…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization.
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
Geometric quantization procedures go usually through an extension of the original theory (pre-quantization) and a subsequent reduction (selection of the physical states). In this context we describe a full geometrical mechanism which…
Characterization of mixed quantum states represented by density operator is one of the most important task in quantum information processing. In this work we will present a geometric approach to characterize the density operator in terms of…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
In this paper we study the state determination for composite systems of two spatial qubits. We show, theoretically, that one can use the technique of quantum tomography to reconstruct the density matrixes of these systems. This tomographic…
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…