Probing the geometry of two-qubit state space by evolution

We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types of evolution in terms of the defining parameters and obtain r...

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Bibliographic Details
Published in:arXiv.org 2018-09
Main Authors: Frydryszak, Andrzej M, Gieysztor, Maria, Kuzmak, Andrij
Format: Article
Language:English
Subjects:
Evolution
Geometry
Hamiltonian functions
Manifolds (mathematics)
Parameters
Quantum entanglement
Quantum theory
Qubits (quantum computing)
Online Access:Get full text
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Summary:We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types of evolution in terms of the defining parameters and obtain relevant explicit description of the pure state spaces and their Remannian geometry with the Fubini-Study metric . In particular, there is given an analysis of the modification of known geometry of quantum state manifold by the linear noncommuting perturbation of the Hamiltonian. For families of states resulting from the unitary evolution, we characterize a degree of entanglement using the squared concurrence as its measure.
ISSN:2331-8422
DOI:10.48550/arxiv.1809.00731