Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

Area of Science:

• Quantum physics
• Topological states of matter
• Quantum information science

Background:

• Non-Hermitian topological edge states are complex and primarily studied via bulk-boundary correspondence.
• Existing methods for analyzing these states often rely on engineered boundaries, limiting broader applicability.

Purpose of the Study:

• To propose and investigate diffusion coefficients as a bulk property for probing topological states in quantum walks.
• To explore the dynamics of topological states using diffusion coefficients in both Hermitian and non-Hermitian systems.

Main Methods:

• Utilizing discrete-time quantum walks, both Hermitian and parity-time (PT)-symmetric non-Hermitian.
• Analyzing the behavior of diffusion coefficients across topological phase transitions.
• Examining the correlation between Shannon entropy and diffusion coefficients.

Main Results:

• Diffusion coefficients exhibit unique features signaling topological phase transitions in both Hermitian and non-Hermitian quantum walks.
• Hermitian systems show a distinct turning point in diffusion coefficients near transitions.
• Non-Hermitian systems, particularly in the PT-symmetric-broken phase, display an abrupt change with a peak in diffusion coefficients.

Conclusions:

• Diffusion coefficients offer a novel, boundary-independent approach to identify and study topological states.
• The findings suggest a new pathway for exploring topological phenomena in non-Hermitian quantum walk systems.
• Direct correlation between Shannon entropy and diffusion coefficients provides further insight into quantum walk dynamics.