scholarly journals Symmetric states: local unitary equivalence via stabilizers

2010 ◽  
Vol 10 (11&12) ◽  
pp. 1029-1041
Author(s):  
Curt D. Cenci ◽  
David W. Lyons ◽  
Laura M. Snyder ◽  
Scott N. Walck
Keyword(s):  
Degrees Of Freedom ◽  
Rotation Group ◽  
Equivalence Classes ◽  
Unitary Equivalence ◽  
Finite Subgroups ◽  
Local Unitary Equivalence ◽  
Symmetric States

We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups. For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom, the classification is exhaustive. We show that local unitary stabilizer groups with no continuous degrees of freedom are isomorphic to finite subgroups of the rotation group $SO(3)$, and give examples of states with discrete stabilizers.

scholarly journals Human Hand Anatomy-Based Prosthetic Hand

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 137
Author(s):  
Larisa Dunai ◽  
Martin Novak ◽  
Carmen García Espert
Keyword(s):  
3D Printing ◽  
Degrees Of Freedom ◽  
Use Of Force ◽  
Hand Movements ◽  
Human Hand ◽  
Prosthetic Hand ◽  
Object Surface ◽  
Hand Phalanges ◽  
High Level

The present paper describes the development of a prosthetic hand based on human hand anatomy. The hand phalanges are printed with 3D printing with Polylactic Acid material. One of the main contributions is the investigation on the prosthetic hand joins; the proposed design enables one to create personalized joins that provide the prosthetic hand a high level of movement by increasing the degrees of freedom of the fingers. Moreover, the driven wire tendons show a progressive grasping movement, being the friction of the tendons with the phalanges very low. Another important point is the use of force sensitive resistors (FSR) for simulating the hand touch pressure. These are used for the grasping stop simulating touch pressure of the fingers. Surface Electromyogram (EMG) sensors allow the user to control the prosthetic hand-grasping start. Their use may provide the prosthetic hand the possibility of the classification of the hand movements. The practical results included in the paper prove the importance of the soft joins for the object manipulation and to get adapted to the object surface. Finally, the force sensitive sensors allow the prosthesis to actuate more naturally by adding conditions and classifications to the Electromyogram sensor.

Entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states

2014 ◽  
Vol 14 (11&12) ◽  
pp. 937-948
Author(s):  
Eylee Jung ◽  
DaeKil Park
Keyword(s):  
Separable States ◽  
Qubit System ◽  
Symmetric States

In this paper we analyze entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states $\rho^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $\rho^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the relaxed Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of $\rho^{ES}$ are not dependent on $y_j \hspace{.2cm} (j=1,2,3)$ individually, but dependent on $y_1 + y_2 + y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

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