Quantum communication protocols by quantum walks with two coins

¹ Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Beijing, 100190, China
² NCMIS, MDIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Beijing, 100190, China
³ School of Mathematical Sciences, University of Chinese Academy of Sciences-Beijing, 100049, China
⁴ Key Lab of IIP, Institute of Computing Technology, Chinese Academy of Sciences - Beijing, 100190, China

^(a) shangyun@amss.ac.cn (corresponding author)
^(b) ming-happy@163.com
^(c) limeng162@mails.ucas.ac.cn
^(d) rqlu@math.ac.cn

Received: 22 August 2018
Accepted: 6 December 2018

Abstract

We introduce some new perfect state transfer and generalized long-distance teleportation schemes by quantum walks with two coins. By encoding the transferred information in the coin-1 state and alternately using two coin operators, we can perfectly recover the information in the coin-1 state at the target position by at most two flipping operations. On the basis of quantum walks with two coins on either a line or an N-circle, we can perfectly transfer any qubit state. In addition, using quantum walks with two coins on regular graphs, we can first implement a perfect qudit state transfer by quantum walks. Compared with existing schemes driven by one coin, more general graph structures can be used to perfectly transfer a more general state. We also study how to realize generalized teleportation over long-distance walks by the above quantum walk models.