Discrete-Time Quantum Walk with Phase Disorder: Localization and Entanglement Entropy

Area of Science:

• Quantum physics
• Condensed matter physics
• Quantum information science

Background:

• Quantum walks (QW) show distinct transport properties compared to classical walks due to quantum interference.
• Phase disorder is a key factor affecting quantum transport phenomena.

Purpose of the Study:

• Investigate the effects of static/dynamic phase disorder on discrete-time quantum walks (DTQW) in 1D and 2D.
• Analyze how different coin types (Hadamard, Grover) and disorder distributions impact DTQW transport properties.

Main Methods:

• Simulated discrete-time quantum walks (DTQW) in one and two dimensions.
• Introduced on-site static and dynamic phase disorder with binary and uniform distributions.
• Employed Hadamard and Grover coins for quantum operations.
• Quantified transport properties using inverse participation ratio (IPR) and standard deviation of the density function (σ).
• Calculated coin-position entanglement entropy (EE).

Main Results:

• DTQW transport properties are sensitive to dimensionality, coin type, and disorder dynamics (static vs. dynamic).
• The distribution type (binary vs. uniform) of phase disorder has a negligible effect on the quantum walk.
• Observed distinct behaviors in 1D and 2D systems, influenced by the chosen coin operators.

Conclusions:

• Dimensionality, coin choice, and disorder nature are critical factors governing DTQW behavior.
• Phase disorder distribution is not a primary driver of observed transport phenomena in these DTQW models.
• The study highlights the complex interplay between system parameters and quantum transport in disordered quantum walks.