Modeling the effects of perturbations and steepest entropy ascent on the time evolution of entanglement

This work presents an analysis of the evolution of perturbed Bell diagonal states using the equation of motion of steepest-entropy-ascent quantum thermodynamics (SEAQT), the Lindblad equation, and various measures of loss of entanglement. First, a brief derivation is presented showing that Bell diagonal states are stationary states that are not stable equilibrium states relative to the SEAQT equation of motion, highlighting the need for the development of perturbation methods to study the evolutions of nearby states. This contrasts with the Lindblad equation of motion for which only some of the Bell diagonal states are stationary. Next, two perturbation methods are presented. The first is a weighted-average method for perturbing bi-partite system states and the second is a general bi-partite method based on a set of unitary operations that are constrained to hold the system energy and system entropy constant. Sets of density operators are randomly generated with each method and the resulting time-varying characteristics of the system's entanglement are analyzed using the SEAQT and Lindblad frameworks. The findings reveal that the evolutions associated with the constrained perturbations accurately predict the loss of non-locality and align well with the measured concurrence. In addition, using the SEAQT framework, the deep connection between the thermodynamic states of the state evolution of the system and the loss of non-locality is quantitatively demonstrated.
Comment: 15 Pages, 14 Figures