Abstract
We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the probability distribution in the QRW emerges. Different localized behaviors of the probability distribution in the QRW are presented when the defect occupies different positions. Given that the coefficients of the localized stationary eigenstates relies on the coin operator, we reveal that when the defect occupies different positions, the amplitude of localized probability distribution in the QRW exhibits a non-trivial dependence on the coin operator.
Highlights
We study the localization of probability distribution in a discrete quantum random walk on an infinite chain
We have studied the localization of the position distribution in the quantum random walk (QRW) on an infinite chain
When the single phase defect is introduced into any position of the QRW, the probability at that position where the defect occupies does not tend to zero in the infinite time limit, and the localization of the probability distribution in the QRW emerges
Summary
We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. An interesting result is presented that when the defect occupies different positions, the amplitude of localized probability in the QRW reflects the non-trivial dependence on the parameter θ of the coin operator C(θ), shows a simple monotonic increase with the parameter θ as reported before[62]. Such property that the probability distribution of the QRW depends on the coin operator is very significant and has its application into the development of the quantum algorithms[23,24,25,26,27].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
