Robustness and classical proxy of entanglement in variants of quantum walks

被引:0
|
作者
Mastandrea, Christopher [1 ]
Chien, Chih-Chun [1 ]
机构
[1] Department of Physics, University of California, Merced,CA,95343, United States
基金
美国国家科学基金会;
关键词
Coin operated equipment - Inverse problems - Population statistics - Quantum optics;
D O I
10.1103/PhysRevE.110.064124
中图分类号
学科分类号
摘要
A quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QWs with the conventional, symmetric, and split-step translation operators with or without classical randomness in the coin operator, we show the entanglement is robust against both time- and spatially dependent randomness, which can cause localization transitions of QWs. We propose a classical quantity called overlap, which literally measures the overlap between the probability distributions of the internal states as a proxy of entanglement. The overlap is associated with the off-diagonal terms of the reduced density matrix in the internal space, which then reflects its purity. Therefore, the overlap captures the inverse behavior of the entanglement entropy in most cases. We test the limitation of the classical proxy by constructing a special case with high population imbalance between the internal states to blind the overlap. Possible implications and experimental measurements are also discussed. © 2024 American Physical Society.
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