Extremal Density Matrices for the Expectation Value of a Qudit Hamiltonian

Quantum Fest 2016 International Conference on Quantum Phenomena, Quantum Control and Quantum Optics

Castaños, O.^1 ; Figueroa, A.^1 ; López, J.^1 ; López-Peña, R.^1

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, México City

04510, Mexico^1

关键词: Density matrix;    Eigenstates;    Energy spectra;    Expectation values;    Hamiltonian matrix;    Neumann equation;    Positivity conditions;    Stationary solutions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/839/1/012012/pdf
DOI  :  10.1088/1742-6596/839/1/012012

来源: IOP

【 摘 要 】

An algebraic procedure to find extremal density matrices for the expectation value of a finite Hamiltonian matrix is established. The extremal density matrices for pure states provide a complete description of the system, that is, its corresponding energy spectrum and projectors. For density matrices representing mixed states, one gets the most probable eigenstates that yield extremal mean values of the energy. The procedure uses mainly the stationary solutions of the von Neumann equation of motion, the orbits of the Hamiltonian, and the positivity conditions of the density matrix. The method is illustrated for matrix Hamiltonians of dimensions d = 2 and d = 3.