scholarly journals Separable states and the structural physical approximation of a positive map

2013 ◽  
Vol 264 (9) ◽  
pp. 2197-2205 ◽  
Author(s):  
Erling Størmer
Keyword(s):  
Positive Map ◽  
Separable States ◽  
Physical Approximation

Some Remarks on the Role of Minimal Length of Positive Maps in Constructing Entanglement Witnesses

2004 ◽  
Vol 11 (04) ◽  
pp. 385-390 ◽  
Author(s):  
A. Jamiołkowski
Keyword(s):  
Hilbert Space ◽  
Minimal Length ◽  
Completely Positive ◽  
Positive Map ◽  
Separable States ◽  
Positive Maps ◽  
Entanglement Witnesses ◽  
Adjoint Operators

The main objective of this paper is to discuss correspondence between the concept of entanglement witnesses (self-adjoint operators on a composite Hilbert space [Formula: see text] that are, in general, not positive, but are positive on separable states) and positive maps [Formula: see text] which are not completely positive. The notion of minimal length of linear positive map is introduced and the role of this quantity in the constructing of entanglement witnesses is explained.

scholarly journals Non-separable states in a bipartite elastic system

AIP Advances ◽  
2017 ◽  
Vol 7 (4) ◽  
pp. 045020 ◽  
Author(s):  
P. A. Deymier ◽  
K. Runge
Keyword(s):  
Elastic System ◽  
Separable States

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.

scholarly journals Understanding What Numbers Mean

2011 ◽  
Author(s):  
Ron Britton
Keyword(s):  
Undergraduate Education ◽  
Functional Characteristics ◽  
Physical Sense ◽  
Physical Approximation ◽  
Do So

As instructors we expect our students to understand what the numbers they generate “mean”. We expect them to be able to visualize, in real or virtual terms, some physical approximation of the “things” they are working with. This visualization provides the basis for a “logic check” on their calculations.Our profession is founded on our ability to specify, within imposed constraints, the physical and functional characteristics of a system that will provide a safe, affordable solution to a problem. Students need to develop and refine this capacity during their undergraduate education. As simple as that may seem to those of us who have experienced the realities of our particular areas of expertise, it is not intuitive. Virtually all academic engineers lament the fact that students regularly submit answers that make no physical sense. The twin questions this issue raises are:1. why do so many students seem to lack an understanding of what their computer generated numbers mean?, and2. how can we help them gain the understanding we want them to have?

scholarly journals CUNTZ–KRIEGER ALGEBRAS AND ONE-SIDED CONJUGACY OF SHIFTS OF FINITE TYPE AND THEIR GROUPOIDS

2019 ◽  
Vol 109 (3) ◽  
pp. 289-298
Author(s):  
KEVIN AGUYAR BRIX ◽  
TOKE MEIER CARLSEN
Keyword(s):  
Conjugacy Class ◽  
Finite Type ◽  
Negative Answer ◽  
The Other ◽  
Completely Positive Map ◽  
Completely Positive ◽  
Positive Map ◽  
Shift Of Finite Type ◽  
Abelian Subalgebra ◽  
The One

AbstractA one-sided shift of finite type $(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines on the one hand a Cuntz–Krieger algebra ${\mathcal{O}}_{A}$ with a distinguished abelian subalgebra ${\mathcal{D}}_{A}$ and a certain completely positive map $\unicode[STIX]{x1D70F}_{A}$ on ${\mathcal{O}}_{A}$. On the other hand, $(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines a groupoid ${\mathcal{G}}_{A}$ together with a certain homomorphism $\unicode[STIX]{x1D716}_{A}$ on ${\mathcal{G}}_{A}$. We show that each of these two sets of data completely characterizes the one-sided conjugacy class of $\mathsf{X}_{A}$. This strengthens a result of Cuntz and Krieger. We also exhibit an example of two irreducible shifts of finite type which are eventually conjugate but not conjugate. This provides a negative answer to a question of Matsumoto of whether eventual conjugacy implies conjugacy.

The extreme points of SU(2)-irreducibly covariant channels

2014 ◽  
Vol 25 (06) ◽  
pp. 1450048 ◽  
Author(s):  
M. Al Nuwairan
Keyword(s):  
Extreme Points ◽  
Quantum Channels ◽  
Completely Positive ◽  
Positive Map ◽  
Covariant Quantum ◽  
Kraus Representation ◽  
Dual Map ◽  
Complementary Channel

In this paper, we introduce EPOSIC channels, a class of SU(2)-covariant quantum channels. For each of them, we give a Kraus representation, its Choi matrix, a complementary channel, and its dual map. We show that they are the extreme points of all SU(2)-irreducibly covariant channels. As an application of these channels, we get an example of a positive map that is not completely positive.

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