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Table 2 QIA protocol example when \(n=4\)

From: Quantum identity authentication based on the extension of quantum rotation

Initial state

\(k_{\mathrm{ide}}\)

\(l_{i}\)

\(k_{b}\)

\(k_{\mathrm{app}}\)

\(k_{\mathrm{ver}}\)

\(\vert \Psi{_{\mathrm{app}}}(\theta _{n})\rangle \)

\(\vert \Psi{_{\mathrm{ide}}} (\theta _{n})\rangle\)

\(\vert \Psi{_{\mathrm{ver}}}(\theta _{n})\rangle \)

Results

|0〉

0

1

8

2

6

\(R(\frac{\pi}{4})\vert 0\rangle \)

\(R(\frac{\pi}{4})\vert 0\rangle \)

R(π)|0〉

|1〉

|0〉

1

0

−1

−10

9

\(R(-\frac{5\pi}{4})\vert 0\rangle \)

\(R(-\frac{9\pi}{8})\vert 0\rangle \)

R(0)|0〉

|0〉

|0〉

2

0

−2

−1

−1

\(R(-\frac{\pi}{8})\vert 0\rangle \)

\(R(\frac{\pi}{8})\vert 0\rangle \)

R(0)|0〉

|0〉

|0〉

3

1

5

−11

16

\(R(-\frac{11\pi}{8})\vert 0\rangle \)

R(−π)|0〉

R(π)|0〉

|1〉