scholarly journals Distilling Entanglement from Fermions

2009 ◽  
Vol 16 (02n03) ◽  
pp. 243-258
Author(s):  
Michael Keyl
Keyword(s):  
Hilbert Spaces ◽  
Point Of View ◽  
Entangled States ◽  
Algebraic Point ◽  
Gaussian States ◽  
Free Fermions ◽  
One Dimensional ◽  
Fermionic Systems ◽  
Maximally Entangled States ◽  
Local Observables

Since fermions are based on anti-commutation relations, their entanglement cannot be studied in the usual way, such that the available theory has to be modified appropriately. Recent publications consider in particular the structure of separable and of maximally entangled states. In this paper we want to discuss local operations and entanglement distillation from bipartite fermionic systems. To this end we apply an algebraic point of view where algebras of local observables, rather than tensor product Hilbert spaces play the central role. We apply our scheme in particular to fermionic Gaussian states, where the whole discussion can be reduced to properties of the covariance matrix. Finally, the results are demonstrated with free fermions on an infinite, one-dimensional lattice.

A lattice of extension rings for a commutative ring

1978 ◽  
Vol 84 (2) ◽  
pp. 225-234 ◽  
Author(s):  
D. Kirby ◽  
M. R. Adranghi
Keyword(s):  
Point Of View ◽  
Local Rings ◽  
Algebraic Point ◽  
Multiple Points ◽  
One Dimensional ◽  
Maximal Ideals ◽  
Blowing Up ◽  
Abstract Case ◽  
Algebroid Curve

The work of this note was motivated in the first place by North-cott's theory of dilatations for one-dimensional local rings (see, for example (4) and (5)). This produces a tree of local rings as in (4) which corresponds, in the abstract case, to the branching sequence of infinitely-near multiple points on an algebroid curve. From the algebraic point of view it seems more natural to characterize such one-dimensional local rings R by means of the set of rings which arise by blowing up all ideals Q which are primary for the maximal ideals M of R. This set of rings forms a lattice (R), ordered by inclusion, each ring S of which is a finite R-module. Moreover the length of the R-module S/R is just the reduction number of the corresponding ideal Q (cf. theorem 1 of Northcott (6)). Thus the lattice (R) provides a finer classification of the rings R than does the set of reduction numbers (cf. Kirby (1)).

scholarly journals Generation of hybrid maximally entangled states in a one-dimensional quantum walk

2020 ◽  
Vol 5 (2) ◽  
pp. 025002 ◽  
Author(s):  
Aikaterini Gratsea ◽  
Maciej Lewenstein ◽  
Alexandre Dauphin
Keyword(s):  
Quantum Walk ◽  
Entangled States ◽  
One Dimensional ◽  
Maximally Entangled States

Entanglement concentration for non-maximally entangled states of qudits

2009 ◽  
Vol 282 (7) ◽  
pp. 1482-1487 ◽  
Author(s):  
M. Yang ◽  
A. Delgado ◽  
L. Roa ◽  
C. Saavedra
Keyword(s):  
Entanglement Concentration ◽  
Entangled States ◽  
Maximally Entangled States

Poly[[μ2-1,3-bis(pyridin-4-yl)propane](μ3-1,4-phenylenediacetato)cadmium]

2012 ◽  
Vol 68 (2) ◽  
pp. m34-m36 ◽  
Author(s):  
Dong Liu
Keyword(s):  
Title Complex ◽  
Point Of View ◽  
Solvothermal Reaction ◽  
Dimensional Chain ◽  
Two Dimensional ◽  
One Dimensional ◽  
Connected Network ◽  
Dimensional Network

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.

scholarly journals CONFLICTS AND FAIR TESTING

2006 ◽  
Vol 17 (04) ◽  
pp. 797-813 ◽  
Author(s):  
ROBI MALIK ◽  
DAVID STREADER ◽  
STEVE REEVES
Keyword(s):  
Discrete Event Systems ◽  
Process Algebra ◽  
Discrete Event ◽  
Denotational Semantics ◽  
Point Of View ◽  
Algebraic Point ◽  
Event Systems ◽  
Common Task ◽  
Testing Theory ◽  
Process Algebraic

This paper studies conflicts from a process-algebraic point of view and shows how they are related to the testing theory of fair testing. Conflicts have been introduced in the context of discrete event systems, where two concurrent systems are said to be in conflict if they can get trapped in a situation where they are waiting or running endlessly, forever unable to complete their common task. In order to analyse complex discrete event systems, conflict-preserving notions of refinement and equivalence are needed. This paper characterises an appropriate refinement, called the conflict preorder, and provides a denotational semantics for it. Its relationship to other known process preorders is explored, and it is shown to generalise the fair testing preorder in process-algebra for reasoning about conflicts in discrete event systems.

Infinitely entangled states

2003 ◽  
Vol 3 (4) ◽  
pp. 281-306
Author(s):  
M. Keyl ◽  
D. Schlingemann ◽  
R.F. Werner
Keyword(s):  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Entangled States ◽  
Entangled State ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Density Operators ◽  
Fundamental Paper ◽  
Extended Notion

For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as a resource for tasks like the teleportation of arbitrarily many qubits. We show that appropriate states cannot be obtained by density operators in an infinite dimensional Hilbert space. However, using techniques for the description of infinitely many degrees of freedom from field theory and statistical mechanics, such states can nevertheless be constructed rigorously. We explore two related possibilities, namely an extended notion of algebras of observables, and the use of singular states on the algebra of bounded operators. As applications we construct the essentially unique infinite analogue of maximally entangled states, and the singular state used heuristically in the fundamental paper of Einstein, Rosen and Podolsky.

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