Name
Abstract | ||
|---|---|---|
Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We deal with the right eigenvalue problem of quaternionic matrices in order to study spectra of the transition matrix of a quaternionic quantum walk. The way to obtain all the right eigenvalues of a quaternionic matrix is given. From the unitary condition on the transition matrix of a quaternionic quantum walk, we deduce some remarkable properties of it. Our main results determine all the right eigenvalues of the quaternionic quantum walk by using those of the corresponding weighted matrix. In addition, we give some examples of quaternionic quantum walks and their right eigenvalues. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s11128-015-1205-8 | Quantum Information Processing |
Keywords | Field | DocType |
Quantum walk,Ihara zeta function,Quaternion,Quaternionic quantum walk,60F05,05C50,15A15,11R52 | Quaternionic representation,Stochastic matrix,Matrix (mathematics),Quantum mechanics,Quaternion,Ihara zeta function,Quantum walk,Unitary state,Eigenvalues and eigenvectors,Physics | Journal |
Volume | Issue | ISSN |
15 | 2 | 1570-0755 |
Citations | PageRank | References |
2 | 0.44 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Norio Konno | 1 | 125 | 29.90 |
| hideo mitsuhashi | 2 | 2 | 0.44 |
| Iwao Sato | 3 | 75 | 22.91 |