Invariants and polynomial identities for higher rank matrices

Tapia, Víctor

doi:10.1088/1751-8113/40/21/005

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…The upper bound defines the most mixed state with maximum von Neumann entropy, while the lower bound specifies pure states which has zero entropy. Additionally, it is known that a k = 0 for all values of k > rank(ρ) [24].…”

Section: A Positivity Conditions For the Density Operatormentioning

confidence: 99%

Entanglement of extremal density matrices of 2-qubit Hamiltonian with Kramers degeneracy

Figueroa,

Castanos,

Lopez-Pena

2018

Preprint

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We establish a novel procedure to analyze the entanglement properties of extremal density matrices depending on the parameters of a finite dimensional Hamiltonian. It was applied to a general 2-qubit Hamiltonian which could exhibit Kramers degeneracy. This is done through the extremal density matrix formalism, which allows to extend the conventional variational principle to mixed states. By applying the positive partial transpose criterion in terms of the Correlation and Schlienz-Mahler matrices on the extremal density matrices, we demonstrate that it is possible to reach both pure and mixed entangled states, changing properly the parameters of the Hamiltonian. For time-reversal invariant Hamiltonians, the extremal pure states can be entangled or not and we prove that they are not time-reversal invariants. For extremal mixed states we have in general 5 possible cases: three of them are entangled and the other two separable.

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Section: A Positivity Conditions For the Density Operatormentioning

confidence: 99%

Entanglement of extremal density matrices of 2-qubit Hamiltonian with Kramers degeneracy

Figueroa,

Castanos,

Lopez-Pena

2018

Preprint

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“…which is due to the fact that the construction of an even rank tensor as the direct product of an original odd-rank tensor is the recipe to define the determinant of the odd-rank tensor [23,24,25].…”

Section: Torsional Extension To Ricci Determinantmentioning

confidence: 99%

“…( 107) is not the end for us, that is to say, we can express the Kronecker delta definitions for that term. To do this, it is enough to consider the inverse Riemann expression [23,24,25]…”

Section: Riemannian Action Based On the Affine Connectionmentioning

confidence: 99%

Affine dynamics with torsion

Gültekin

2016

Eur. Phys. J. C

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In this study, we give a thorough analysis of a general affine gravity with torsion. After a brief exposition of the affine gravities considered by Eddington and Schrödinger, we construct and analyze different affine gravities based on the determinants of the Ricci tensor, the torsion tensor, the Riemann tensor and their combinations. In each case we reduce equations of motion to their simplest forms and give a detailed analysis of their solutions. Our analyses lead to the construction of the affine connection in terms of the curvature and torsion tensors. Our solutions of the dynamical equations show that the curvature tensors at different points are correlated via non-local, exponential rescaling factors determined by the torsion tensor.

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Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules

Rey

2019

The Journal of Chemical Physics

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Invariants and polynomial identities for higher rank matrices

Cited by 3 publications

References 23 publications

Entanglement of extremal density matrices of 2-qubit Hamiltonian with Kramers degeneracy

Entanglement of extremal density matrices of 2-qubit Hamiltonian with Kramers degeneracy

Affine dynamics with torsion

Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules

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