This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association scheme. Our focus includes specific association schemes, namely the Hamming and Johnson schemes. We characterize all graphs on the classes of Hamming and Johnson schemes that exhibit perfect state transfer. Furthermore, we study perfect state transfer on distance-regular graphs. We provide complete characterizations for exhibiting perfect state transfer on distance-regular graphs of diameter $2$ and diameter $3$ , as well as integral distance-regular graphs.This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association scheme. Our focus includes specific association schemes, namely the Hamming and Johnson schemes. We characterize all graphs on the classes of Hamming and Johnson schemes that exhibit perfect state transfer. Furthermore, we study perfect state transfer on distance-regular graphs. We provide complete characterizations for exhibiting perfect state transfer on distance-regular graphs of diameter $2$ and diameter $3$, as well as integral distance-regular graphs.

arXiv:2506.07439Jun 9, 20250 citations

Conclusive and perfect quantum state transfer with a single spin chain

Jiankui He, Qing Chen, Lei Ding +1 more

Physics Letters AMay 9, 20071 citation

Perfect state transfer on weighted graphs of the Johnson scheme

Luc Vinet, Hanmeng Zhan

arXiv:1904.08838Letters in Mathematical PhysicsJun 17, 20204 citations

Perfect transfer of m-qubit GHZ states

M. A. Jafarizadeh, Rahime Sufiani, Seyed Farid Taghavi +1 more

By using some techniques such as spectral distribution and stratification associated with the graphs, employed in [1,2] for the purpose of Perfect state transfer (PST) of a single qubit over antipodes of distance-regular spin networks and PST of a $d$ -level quantum state over antipodes of pseudo-distance regular networks, PST of an m-qubit GHZ state is investigated. To do so, we employ the particular distance-regular networks (called Johnson networks) J(2m,m) to transfer an m-qubit GHZ state initially prepared in an arbitrary node of the network (called the reference node) to the corresponding antipode, perfectly. Keywords: Perfect state transferenc, GHZ states, Johnson network, Stratification, Spectral distribution PACs Index: 01.55.+b, 02.10.YnBy using some techniques such as spectral distribution and stratification associated with the graphs, employed in [1,2] for the purpose of Perfect state transfer (PST) of a single qubit over antipodes of distance-regular spin networks and PST of a $d$-level quantum state over antipodes of pseudo-distance regular networks, PST of an m-qubit GHZ state is investigated. To do so, we employ the particular distance-regular networks (called Johnson networks) J(2m,m) to transfer an m-qubit GHZ state initially prepared in an arbitrary node of the network (called the reference node) to the corresponding antipode, perfectly. Keywords: Perfect state transferenc, GHZ states, Johnson network, Stratification, Spectral distribution PACs Index: 01.55.+b, 02.10.Yn

arXiv:0805.1866May 13, 20081 citation

Perfect swap and transfer of arbitrary quantum states

Yusef Maleki, Aleksei M. Zheltikov

Optics CommunicationsFeb 17, 202110 citations

2

and diameter

3

, as well as integral distance-regular graphs.

d

-level quantum state over antipodes of pseudo-distance regular networks, PST of an m-qubit GHZ state is investigated. To do so, we employ the particular distance-regular networks (called Johnson networks) J(2m,m) to transfer an m-qubit GHZ state initially prepared in an arbitrary node of the network (called the reference node) to the corresponding antipode, perfectly. Keywords: Perfect state transferenc, GHZ states, Johnson network, Stratification, Spectral distribution PACs Index: 01.55.+b, 02.10.Yn