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Sub-Geometric Phases in Density Matrices.

Zheng-Chuan Wang¹

¹Department of Physics & CAS Center for Excellence in Topological, Quantum Computation, The University of Chinese Academy of Sciences, P. O. Box 4588, Beijing, 100049, China. wangzc@ucas.ac.cn.

Scientific Reports

|September 15, 2019

Summary

This summary is machine-generated.

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This study unifies geometric phase expressions for density matrices in both adiabatic and non-adiabatic processes. It reveals the impact of sub-geometric phases on physical observables, including in mixed states.

Area of Science:

Quantum Mechanics
Quantum Information Theory

Background:

Geometric phases, such as the Berry and Aharonov-Anandan phases, are fundamental concepts in quantum mechanics.
Understanding these phases in density matrices is crucial for characterizing quantum states and processes.

Purpose of the Study:

To generalize the concept of geometric phases to density matrices.
To unify the expressions for extended sub-geometric phases in both adiabatic and non-adiabatic processes.
To investigate the influence of these phases on physical observables and their application to mixed states.

Main Methods:

Development of a unified expression for the extended sub-geometric phase.
Establishment of relationships between extended sub-geometric phases and established Berry/Aharonov-Anandan phases.

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Analysis of the impact of sub-geometric phases on measurable physical quantities.

Main Results:

A unified expression for the extended sub-geometric phase applicable to both adiabatic and non-adiabatic evolutions was derived.
The study established clear relations between the extended sub-geometric phase and the standard Berry and Aharonov-Anandan phases.
The influence of sub-geometric phases on physical observables was demonstrated, with applications to mixed quantum states.

Conclusions:

The generalization of geometric phases to density matrices provides a unified framework for understanding quantum phase phenomena.
Sub-geometric phases play a significant role in the behavior of physical observables, even in mixed quantum states.