Authors :
Debopam Ghosh
Volume/Issue :
Volume 7 - 2022, Issue 7 - July
Google Scholar :
https://bit.ly/3IIfn9N
Scribd :
https://bit.ly/3BTfNKy
DOI :
https://doi.org/10.5281/zenodo.6974539
Abstract :
The article presents a mathematical
framework to associate a Matrix Shell system (even type
or of the odd type) with a unit trace, hermitian, positive
definite or positive semi-definite matrix of order ‘2’
(Density matrix representation of single qubit quantum
states). This framework therefore, allows any evolution
scheme defined on the fundamental matrix space
associated with the Matrix Shell system and consistent
with the Matrix shell model formalism to be mapped to
an evolution on or inside of the unit solid sphere,
centered at the origin, in the three dimensional space(
Bloch sphere representation of single qubit quantum
states)
Demonstration of the proposed mathematical
framework is presented through its application on
certain subsets of the Complex Matrix spaces M2×2(C)
and M4×4(C) and on certain numerical examples from
M3×3(C)
Keywords :
Matrix Shell Model formalism, Composite pathways, Directional states, State-Interaction Matrix description of Matrix shells and of the Matrix Shell system, Density matrix representation of quantum states, Bloch sphere representation of single qubit quantum states.
The article presents a mathematical
framework to associate a Matrix Shell system (even type
or of the odd type) with a unit trace, hermitian, positive
definite or positive semi-definite matrix of order ‘2’
(Density matrix representation of single qubit quantum
states). This framework therefore, allows any evolution
scheme defined on the fundamental matrix space
associated with the Matrix Shell system and consistent
with the Matrix shell model formalism to be mapped to
an evolution on or inside of the unit solid sphere,
centered at the origin, in the three dimensional space(
Bloch sphere representation of single qubit quantum
states)
Demonstration of the proposed mathematical
framework is presented through its application on
certain subsets of the Complex Matrix spaces M2×2(C)
and M4×4(C) and on certain numerical examples from
M3×3(C)
Keywords :
Matrix Shell Model formalism, Composite pathways, Directional states, State-Interaction Matrix description of Matrix shells and of the Matrix Shell system, Density matrix representation of quantum states, Bloch sphere representation of single qubit quantum states.
