Probing the geometry of two-qubit state space by evolution

We provide explicit geometric description of state manifolds obtained from evolution governed by a four-parameter family of time-independent Hamiltonians. We cover most cases related to the real interacting two-qubit systems and discuss possible types of evolutions in terms of the defining parameter...

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Bibliographic Details
Published in:Quantum information processing 2019-03, Vol.18 (3), p.1-18, Article 84
Main Authors: Frydryszak, Andrzej M., Gieysztor, Maria, Kuzmak, Andrij
Format: Article
Language:English
Subjects:
Data Structures and Information Theory
Evolution
Geometry
Hamiltonian functions
Manifolds (mathematics)
Mathematical Physics
Parameters
Physics
Physics and Astronomy
Quantum Computing
Quantum entanglement
Quantum Information Technology
Quantum Physics
Quantum theory
Qubits (quantum computing)
Spintronics
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Summary:We provide explicit geometric description of state manifolds obtained from evolution governed by a four-parameter family of time-independent Hamiltonians. We cover most cases related to the real interacting two-qubit systems and discuss possible types of evolutions in terms of the defining parameters. The relevant description of the pure state spaces and their Riemannian geometry with the Fubini–Study metric is given. In particular, we analyze the modification of known geometry of quantum state manifold by the linear noncommuting perturbation of the Hamiltonian. Finally, we investigate the behavior of the entanglement for obtained families of states resulting from the unitary evolution.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-019-2199-4