Effect of Quantum Coins on Two-Particle Quantum Walks

Shu Gan, Xingdao He, Bin Liu +1 more

We numerically study the effect of the quantum coins on the two-particle quantum walks on an infinite line. Both non-interacting and interacting particles are considered. The joint probability as well as the bunching or anti-bunching behavior are greatly affected by the phase factors in the coin operation. Further, the spatial correlation can be maximized by choosing appropriate coin parameters. The entanglement between the two particles can be adjusted in the same manner.

G. R. Carson, T. Loke, Jingbo B. Wang

Meng Zeng, Ee Hou Yong

Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.

赵静, 胡亚运, 童培庆

Rashid Ahmad, Uzma Sajjad, Muhammad Sajid

Abstract We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle, which depends upon the position of a quantum particle, parameterizes the coin operator. For different values of the rotation angle, we observe that such a coin leads to a variety of probability distributions, e.g. localized, periodic, classical-like, semi-classical-like, and quantum-like. Further, we study the Shannon entropy associated with position and the coin space of a quantum particle, and compare them with the case of the position-independent coin. Our results show that the entropy is smaller for most values of the rotation angle as compared to the case of the position-independent coin. We also study the effect of entanglement on the behavior of probability distribution and Shannon entropy by considering a quantum walk with two identical position-dependent entangled coins. We observe that in general, a wave function becomes more localized as compared to the case of the position-independent coin and hence the corresponding Shannon entropy is lower. Our results show that a position-dependent coin can be used as a controlling tool of quantum walks.

Jamie Smith