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 Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

Green’s function–based surrogate model for windfields using limited samples

2017 ◽  
Vol 42 (3) ◽  
pp. 164-176 ◽  
Author(s):  
Joshua Paul Marshall ◽  
Joseph David Richardson ◽  
Carlos Jose Montalvo
Keyword(s):  
Green’S Function ◽  
Wind Velocity ◽  
Green's Function ◽  
Surrogate Model ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Fast Method ◽  
Three Dimensional Model ◽  
Wind Velocities ◽  
Wind Measurements

There exists many applications for which wind-velocity is desired over a three-dimensional space. The vector field associated with these wind velocities is known as a “windfield” or “velocity-windfield.” The present work provides a fast method to characterize windfields. The approach uses the free-space Green’s function for potential theory as an inexpensive surrogate model in lieu of either complicated physics-based models or other types of surrogate models, both of which require volumetric discretizations for the three-dimensional case. Using the gradient of the third Green’s identity, the wind-velocity in the interior of a domain is entirely characterized by a surface discretization while still providing a three-dimensional model. The unknown densities on the surface are determined from enforcement of the interior form of the identity at arbitrary points coinciding with wind measurements taken by unmanned aerial vehicles. Numerical results support the feasibility of the method.

Assessment of cross-laminated timber panels by the state-space approach

2019 ◽  
Vol 22 (11) ◽  
pp. 2375-2391
Author(s):  
Asad S Albostami ◽  
Zhangjian Wu ◽  
Lee S Cunningham
Keyword(s):  
State Space ◽  
Three Dimensional ◽  
The State ◽  
Composite Panel ◽  
State Space Approach ◽  
Cross Laminated Timber ◽  
Practical Applications ◽  
The Cross ◽  
Analytical Approaches ◽  
Space Approach

In this article, cross-laminated timber panels are investigated as a novel engineering application of the state-space approach. As cross-laminated timber is a laminated composite panel, the three-dimensional analytical method provided by the state-space approach offers the potential for improved accuracy over existing common approaches to the analysis of cross-laminated timber. Before focusing on the specific application to cross-laminated timber, the general theory of the state-space approach is outlined. The method is then applied to describe the behaviour of a number of cross-laminated timber panel configurations previously examined experimentally and analytically. In order to demonstrate the capability of the state-space approach in this application, the results are compared with those from various two-dimensional and three-dimensional analytical approaches and finite element modelling briefly. With a view to design, different failure criteria are explored to assess the ultimate strength of the cross-laminated timber panels. The state-space approach demonstrates its superior capability in capturing the nonlinear distribution of the elastic stresses through the thickness of the cross-laminated timber panels over a range of span-to-thickness ratios common in practical applications.

scholarly journals Stress analysis of a second stage gas turbine blade under asymmetric thermal gradient

2019 ◽  
Vol 20 (6) ◽  
pp. 607
Author(s):  
Javad Rahimi ◽  
Esmaeil Poursaeidi ◽  
Ehsan Khavasi
Keyword(s):  
Stress Distribution ◽  
Turbine Blade ◽  
Three Dimensional ◽  
Element Model ◽  
The State ◽  
Three Dimensional Model ◽  
Cooling Mode ◽  
Cooling Channels ◽  
Second Stage ◽  
Main Factor

In this study the main causes of the failure of a GE-F9 second stage turbine blade were investigated. The stress distribution of the blade which has 6 cooling vents in three modes (with full cooling, closure of half of the cooling channels, and without cooling) was studied. A three dimensional model of the blade was built and the fluid flow on the blade was studied using the FVM method. The stress distribution due to centrifugal forces applied to the blade, temperature gradients and aerodynamic forces on the blade surface was calculated by the finite element model. The results show that the highest temperature gradient and as a result the highest stress value occurs for the semi-cooling state at the areas near the blade root and this status is true for the full cooling mode for the regions far from the root. However, the field observations showed that the failure occurred for the blade with the semi-cooling state (due to closure of some of the channels) at areas far from the root. It is discussed that the main factor of the failure is not the stress values being maximum because in the state of full cooling mode (the state with the maximum stress values) the temperature of the blade is the lowest state and as a result the material properties of the blade show a better resistance to phenomena like hot corrosion and creep.

Efficient photon sorter in a high-dimensional state space

2011 ◽  
Vol 11 (3&4) ◽  
pp. 313-325
Author(s):  
Warner A. Miller
Keyword(s):  
Quantum Information ◽  
State Space ◽  
Quantum Key Distribution ◽  
Quantum Information Processing ◽  
Three Dimensional ◽  
High Dimensional ◽  
Coupled Mode Theory ◽  
Coupled Mode ◽  
Dimensional State Space ◽  
Significant Obstacle

An increase in the dimension of state space for quantum key distribution (QKD) can decrease its fidelity requirements while also increasing its bandwidth. A significant obstacle for QKD with qu$d$its ($d\geq 3$) has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both amplitude and phase. We propose such a sorter based on a multiplexed thick hologram, constructed e.g. from photo-thermal refractive (PTR) glass. We validate this approach using coupled-mode theory with parameters consistent with PTR glass to simulate a holographic sorter. The model assumes a three-dimensional state space spanned by three tilted planewaves. The utility of such a sorter for broader quantum information processing applications can be substantial.

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.

Stereopsis and the Representation of Space

Perception ◽  
1977 ◽  
Vol 6 (3) ◽  
pp. 327-332 ◽  
Author(s):  
Raymond Klein
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Normal Subjects ◽  
Picture Plane ◽  
Perceptual System ◽  
System A ◽  
Mental Rotations ◽  
Important Input ◽  
Better Than ◽  
Three Dimensional Space

Four stereoblind and four normal subjects were tested on a mental rotation task. It was hypothesized that, if stereopsis is an important input for building up the perceptual system that represents three-dimensional space, then subjects lacking it ought to be deficient at mental rotations in depth. Stereoblind subjects were equally efficient at picture-plane and depth rotations, and were nonsignificantly better than normal subjects at rotations in depth. It was concluded that in the absence of stereopsis other cues are sufficient for the development of the ‘three-dimensional’ perceptual system. A puzzling paradox was raised, however, by the finding that the introspections of the two groups differed markedly.

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