Quantum identity authentication based on the extension of quantum rotation

EPJ Quantum Technology

Table 1 Geometric significance of quantum rotation

Initial state	Rotation direction¹	Final quantum state²
\|0〉	Clockwise	\(R(\theta )\vert 0\rangle =\cos(\frac{\theta}{2})\vert 0\rangle +\sin(\frac{\theta}{2})\vert 1\rangle \)
\|0〉	Anti-clockwise	\(R(-\theta )\vert 0\rangle =\cos(\frac{\theta}{2})\vert 0\rangle -\sin(\frac{\theta}{2})\vert 1\rangle \)
\|1〉	Clockwise	\(R(\theta )\vert 1\rangle =-\sin(\frac{\theta}{2})\vert 0\rangle +\cos(\frac{\theta}{2})\vert 1\rangle \)
\|1〉	Anti-clockwise	\(R(-\theta )\vert 1\rangle =-\sin(\frac{\theta}{2})\vert 0\rangle -\cos(\frac{\theta}{2})\vert 1\rangle \)

¹ Rotation direction refers to the direction in the quantum state rotates on the Bloch circle, which takes the direction of −y as the line of sight. ² To better explain the geometric significance of quantum rotation, we denote \(s\theta _{n}\) as θ and set θ>0 in this table.