# Experimental Quantum Message Authentication with Single Qubit Unitary Operation
## 4 Experiment Setup and Measurement Results
This indicates that [PERSON] generates the QMAC state by applying rotation operator \(R_{y}\big{(}-120^{\circ}\big{)}\) and then uses rotation operator \(R_{y}\big{(}-120^{\circ}\pm\pi n/2\big{)}\) to recover the QMAC state, where \(n\) is an integer, because the period of the half-wave plate is \(\pi/2\). The red plots represent the averages of the coincidence counts over one second. In Figure 4b, we recognize that [PERSON]'s encryption and decryption also work well. When the half-wave plate H2/s angle \(b_{i}/4\) is \(-60^{\circ}\), the Hong-Ou-Mandel dip occurs at the half-wave plate H4/s angles \(-b_{i}/4=60^{\circ}\), \(150^{\circ}\). [PERSON] uses rotation operator \(R_{y}\big{(}-60^{\circ}\big{)}\) to re-encrypt the QMAC state, and then he decrypts the re-encrypted QMAC state by applying rotation  
Figure 3: Schematic representation of the experimental setup for the quantum message authentication protocol and an existential forgery. (**a**) Quantum message authentication protocol: the blue box represents [PERSON]’s operation, and the green box represents [PERSON]’s operation. \(m_{i}\) is the rotation angle that indicates message. \(k^{i}_{AB},k^{i}_{H},s_{i}\), and \(b_{i}\) are the same as in Figure 1. (**b**) Existential forgery: [PERSON] can attempt forgery on the quantum message authentication code (QMAC) state pair using Pauli operators when [PERSON] transmits the encrypted QMAC state pair to [PERSON]. operator \(R_{y}\big{(}60^{\lx@math@degree}\pm\pi n/2\big{)}\), where \(n\) is an integer. In Figure 4, the experimental data are the average of 10 measurements per 10 s.  
During this time, the averages of single counts were \(27,000\) and \(27,000\), respectively, and coincidence windows are 5 ns; the maximum value of the coincidence counts after accidental coincidences were removed was 127, and the minimum value was 2. Second, we tested the quantum encryption and decryption. If [PERSON] and [PERSON] are proper users who previously shared secret key sequences \(K_{AB}\) and \(K_{H}\) then the quantum message states \(\ket{M}_{u}\) and \(\ket{M^{\prime}}_{d}\) should be identical. [PERSON] can check the correspondence of these states using the Hong-Ou-Mandel interferometer [38; 39]. Figure 4 shows the experimental results for [PERSON]'s quantum encryption and [PERSON]'s quantum decryption. \(P_{c}\) is the coincidence probability of Hong-Ou-Mandel interference, and \(\overline{P}_{c}=1-P_{c}\) represents the probability of two quantum message states matching. Figure 5a,b represents whether operator \(H\) exists or not, respectively. Although theoretically, the red blocks on the diagonal in both cases should be 100%, experimentally they are greater than 82% and 76%, respectively. On the other hand, the blue blocks off the diagonal, when [PERSON] and [PERSON] share different secret keys \(k^{i}_{AB}\) and \(k^{i}_{H^{\prime}}\ket{M}_{u}\) and \(\ket{M^{\prime}}_{d}\) have different quantum states, and the respective probabilities are less than 41% and less than 46%. Considering that theoretically \(\overline{P}_{c}\) can only have less than 50%, the measurement results prove that our scheme works well. From these results, we can conclude that the encryption operates properly because \(\overline{P}_{c}\) is greater than 76% in the case of the same operators and \(\overline{P}_{c}\) is less than 46% in the case of different operators regardless of the existence of operator \(H\). The above theoretical values are derived from the success probability \(\epsilon^{2}=\big{|}_{d}\langle\psi^{\prime}_{i}|\psi_{i}\rangle\big{|}^{2}\) of the swap test, with \(\ket{\psi_{i}}_{u}=U_{i}R_{y}(m_{i})\ket{0}_{u}^{(i)}\), \(\big{|}\psi^{\prime}_{i}\rangle_{d}=U^{\prime}_{i}R_{y}(m_{i})\ket{0}_{d}^{(i)}\), \(U_{i},U^{\prime}_{i}\in\big{\{}I,\)\(\sigma_{x},\sigma_{y},\sigma_{z}\), \(H\), \(\sigma_{x}H,\sigma_{y}H,\sigma_{z}H\big{\}}\), and \(m_{i}=135^{\circ}\).