Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/13418
Title: Maximally entangled two-qutrit quantum information states and De Gua’s theorem for tetrahedron
Authors: Pashaev, Oktay
Keywords: De Gua’s theorem
Entanglement
Generalized Pythagoras theorem
Quantum information
Qutrit states
Geometry
Quantum optics
Qubits
De gua’s theorem
Entanglement
Generalized pythagora theorem
Geometric relations
Information state
Pythagoras
Quantum Information
Qutrit state
Qutrits
Tetrahedra
Quantum entanglement
Issue Date: 2023
Publisher: Springer
Abstract: Geometric relations between separable and entangled two-qubit and two-qutrit quantum information states are studied. For two qubit states a relation between reduced density matrix and the concurrence allows us to characterize entanglement by double area of a parallelogram, expressed by determinant of the complex Hermitian inner product metric. We find similar relation in the case of generic two-qutrit state, where the concurrence is expressed by sum of all 2 × 2 minors of 3 × 3 complex matrix. We show that for maximally entangled two-retrit state this relation is just De Gua’s theorem or a three-dimensional analog of the Pythagorean theorem for triorthogonal tetrahedron areas. Generalizations of our results for arbitrary two-qudit states are discussed © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Description: 3rd International Conference on Mathematics and its Applications in Science and Engineering, ICMASE 2022 -- 4 July 2022 through 7 July 2022 -- 291239
URI: https://doi.org/10.1007/978-3-031-21700-5_10
https://hdl.handle.net/11147/13418
ISBN: 9783031216992
ISSN: 2194-1009
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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