Related papers: Quantum Geometric Tensor for Mixed States Based on…
We introduce and explore the notion of texture of an arbitrary quantum state, in a selected basis. In the first part of this letter we develop a resource theory and show that state texture is adequately described by an easily computable…
Pure three-qubit states have five algebraically independent and one algebraically dependent polynomial invariants under local unitary transformations and an arbitrary entanglement measure is a function of these six invariants. It is shown…
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…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
Quantum metrology exploits quantum mechanical effects to increase the precision of measurements of physical quantities. A wide variety of applications are currently being developed for scientific and technological purposes, however, most…
We examine the geodesic between two mixed states of arbitrary dimension by means of their geometric mean operator. We utilize the fiber bundle approach by which the distance between two mixed state density operators $\rho_1$ and $\rho_2$ in…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
It is known that there are infinitely many distinguishability metrics for mixed quantum states. This freedom, in turn, leads to metric-dependent interpretations of physically meaningful geometric quantities such as complexity and volume of…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
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…
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.
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced…