Quaternionic quantum walks. (English) Zbl 1317.81184
Summary: The discrete-time quantum walk (QW) has been extensively and intensively investigated in the last decade, whose coin operator is defined by a unitary matrix. We extend the QW to a walk determined by a unitary matrix whose component is quaternion. We call this model quaternionic quantum walk (QQW) and present some properties. This paper is the first step for the study on QQWs.
MSC:
| 81S25 | Quantum stochastic calculus |
| 60F05 | Central limit and other weak theorems |
| 60G50 | Sums of independent random variables; random walks |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
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