Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

Degeneracy of Eigenvalues of Reduced Density Matrices and Time-Reversal Invariance for Electron Systems

David A. Micha

Published Dec 1, 1964• 15 citations
Publisher
DOI
10.1063/1.1725783

Related papers

Pseudo-Hermitian Hamiltonians, time-reversal invariance and Kramers degeneracy

G. Scolarici, Luigi Solombrino

arXiv:quant-ph/0207163•Physics Letters A•Oct 1, 2002•22 citations

Eigenvalue Distributions of Reduced Density Matrices

Matthias Christandl, Brent Doran, Stavros Kousidis +1 more

arXiv:1204.0741•Communications in Mathematical Physics•Aug 18, 2014•41 citations

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

Armando Figueroa, Octavio Castaños, Ramón López–Peña

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.

arXiv:1807.00227•Jun 30, 2018•0 citations

On the degeneracies of quantum systems

J. S. Dowker

International Journal of Theoretical Physics•Jan 1, 1973•1 citation

Use of invariants in bounding 2‐fermion reduced density matrix eigenvalues

Mark E. Casida

Abstract The known bounds on the eigenvalues of 2‐Fermion reduced density matrices may be improved by considering unitarily invariant properties of the associated natural geminals and of the system 1‐Fermion reduced density matrix. The polynomial invariants are particularly important, since they may be introduced systematically according to the degree of the polynomials.

International Journal of Quantum Chemistry•Jan 1, 1988•3 citations

Reduced-Density-Matrix Description of Decoherence and Relaxation Processes for Electron-Spin Systems

V. L. Jacobs

Bulletin of the American Physical Society•Mar 7, 2018•0 citations
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.