Geometry of canonical correlation on the state space of a quantum system

1994 ◽  
Vol 35 (2) ◽  
pp. 780-795 ◽  
Author(s):  
Dénes Petz
Keyword(s):  
State Space ◽  
Quantum System ◽  
Canonical Correlation ◽  
The State

Characterizations of symmetric monotone metrics on the state space of quantum systems

2006 ◽  
Vol 6 (7) ◽  
pp. 597-605
Author(s):  
F. Hansen
Keyword(s):  
State Space ◽  
Quantum System ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Classical Case ◽  
Riemannian Metric ◽  
Quantum Systems ◽  
The State ◽  
Stochastic Mappings

The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.

scholarly journals ON THE CURVATURE OF A CERTAIN RIEMANNIAN SPACE OF MATRICES

2000 ◽  
Vol 03 (02) ◽  
pp. 199-212 ◽  
Author(s):  
PETER W. MICHOR ◽  
DÉNES PETZ ◽  
ATTILA ANDAI
Keyword(s):  
Scalar Curvature ◽  
State Space ◽  
Quantum System ◽  
Curvature Tensor ◽  
Riemannian Space ◽  
Riemannian Metric ◽  
Positive Definite ◽  
The State ◽  
Inner Product ◽  
Positive Definite Matrices

Positive definite matrices of trace 1 describe the state space of a finite quantum system. This manifold can be endowed by the physically relevant Bogoliubov–Kubo–Mori inner product as a Riemannian metric. In this paper the curvature tensor and the scalar curvature are computed.

scholarly journals The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 485
Author(s):  
Christopher Eltschka ◽  
Marcus Huber ◽  
Simon Morelli ◽  
Jens Siewert
Keyword(s):  
State Space ◽  
Quantum System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The State ◽  
Level System ◽  
Three Dimensional Model ◽  
System A ◽  
Dimensional State Space ◽  
Geometric Intuition

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.

scholarly journals Probing quantum state space: does one have to learn everything to learn something?

2017 ◽  
Vol 473 (2201) ◽  
pp. 20160866 ◽  
Author(s):  
Claudio Carmeli ◽  
Teiko Heinosaari ◽  
Jussi Schultz ◽  
Alessandro Toigo
Keyword(s):  
State Space ◽  
Quantum System ◽  
Quantum State ◽  
The State ◽  
Membership Problem ◽  
Complete Measurement ◽  
Alternative Means ◽  
Informational Completeness ◽  
Set Up

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

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