Triality invariance in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> superstring

Castellani, Leonardo; Grassi, Pietro Antonio; Sommovigo, Luca

doi:10.1016/j.physletb.2009.06.032

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…in analogy to the conventional three-qubit identity (38). This result for sDet agrees with that of [7].…”

Section: B Three Superqubitssupporting

confidence: 90%

“…Moreover, from a physical point of view, it makes contact with various condensed-matter systems. For example, the three-dimensional representation of OSp(1|2) is encountered in the supersymmetric t-J model where it * leron.borsten@imperial.ac.uk † duminda.dahanayake@imperial.ac.uk ‡ m.duff@imperial.ac.uk § william.rubens06@imperial.ac.uk 1 The present work was in part inspired by the construction of the superhyperdeterminant in [7].…”

Section: Introductionmentioning

confidence: 99%

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Superqubits

Borsten

Dahanayake²,

Duff³

et al. 2010

Phys. Rev. D

106

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We provide a supersymmetric generalization of n quantum bits by extending the local operations and classical communication entanglement equivalence group [SU(2)]^n to the supergroup [uOSp(1|2)]^n and the stochastic local operations and classical communication equivalence group [SL(2,C)]^n to the supergroup [OSp(1|2)]^n. We introduce the appropriate supersymmetric generalizations of the conventional entanglement measures for the cases of $n=2$ and $n=3$. In particular, super-Greenberger-Horne-Zeilinger states are characterized by a nonvanishing superhyperdeterminant.Comment: 16 pages, 4 figures, 4 tables, revtex; minor corrections, version appearing in Phys. Rev.

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“…in analogy to the conventional three-qubit identity (38). This result for sDet agrees with that of [7].…”

Section: B Three Superqubitssupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Superqubits

Borsten

Dahanayake²,

Duff³

et al. 2010

Phys. Rev. D

106

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“…The analysis has been extended to include superqubits using a supersymmetric approach based on the theory of Lie superalgebras. In particular, the osp (2|1) Lie superalgebra has been explored to deal with the physics of the superqubits [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Graph theory and qubit information systems of extremal black branes

Belhaj¹,

Sedra²,

Seguí³

2014

J. Phys. A: Math. Theor.

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Using graph theory based on Adinkras, we consider once again the study of extremal black branes in the framework of quantum information. More precisely, we propose a one to one correspondence between qubit systems, Adinkras and certain extremal black branes obtained from type IIA superstring compactified on T n . We accordingly interpret the real Hodge diagram of T n as the geometry of a class of Adinkras formed by 2 n bosonic nodes representing n qubits. In this graphic representation, each node encodes information on the qubit quantum states and the charges of the extremal black branes built on T n . The correspondence is generalized to n superqubits associated with odd and even geometries on the real supermanifold T n|n . Using a combinatorial computation, general expressions describing the number of the bosonic and the fermionic states are obtained.

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Complanart of a system of polynomial equations

Vlasov

2010

Theor Math Phys

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We study homogeneous polynomial maps of vector spaces zi → A i 1 i 2 ...is i zi 1 zi 2 · · · zi s and their eigenvectors and eigenvalues. We define a new quantity called the complanart, which determines the coplanarity of the solution vectors of a system of polynomial equations. Evaluating the complanart reduces to evaluating resultants. As in the linear case, the pattern of eigenvectors/eigenvalues defines the phase diagram of the associated differential equation. Such differential equations arise naturally in attempting to extend Lyapunov's stability theory. The results in this paper can be used in a range of applications from solving nonlinear differential equations and calculating nonlinear exponents to evaluating non-Gaussian integrals.

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Triality invariance in the N=2 superstring

Cited by 5 publications

References 9 publications

Superqubits

Superqubits

Graph theory and qubit information systems of extremal black branes

Complanart of a system of polynomial equations

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