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## <math>C_i</math> applies <math>V^{r_i}U^{x_i}</math> on the received qubit and sends it to client <math>C_{i+1}</math>. | ## <math>C_i</math> applies <math>V^{r_i}U^{x_i}</math> on the received qubit and sends it to client <math>C_{i+1}</math>. | ||
# <math>C_n</math> applies <math>V^{r_n}U^{x_n}</math> on the received qubit. | # <math>C_n</math> applies <math>V^{r_n}U^{x_n}</math> on the received qubit. | ||
# Any client then applies <math>(U^\dagger)^{\oplus_i x_i}</math>. <br> <math>(U^\dagger)^\oplus_i#1_i{x}<br/> \underbrace{V^{r_n}U^{x_n}}_{\mathcal{C}_n} <br/> ... <br/> \underbrace{V^{r_2}U^{x_2}}_{\mathcal{C}_2} <br/> \underbrace{V^{r_1}U^{x_1}}_{\mathcal{C}_1} <br/> \ket{0}= <br/> |r \oplus f\rangle </math> | # Any client then applies <math>(U^\dagger)^{\oplus_i x_i}</math>. <br/> <math>(U^\dagger)^\oplus_i#1_i{x}<br/> \underbrace{V^{r_n}U^{x_n}}_{\mathcal{C}_n} <br/> ... <br/> \underbrace{V^{r_2}U^{x_2}}_{\mathcal{C}_2} <br/> \underbrace{V^{r_1}U^{x_1}}_{\mathcal{C}_1} <br/> \ket{0}= <br/> |r \oplus f\rangle </math> | ||
# The resulting state is now sent to the server who measures the outcome <math>r \oplus f</math> and announces it. | # The resulting state is now sent to the server who measures the outcome <math>r \oplus f</math> and announces it. | ||
# The clients locally compute XOR of the random bits of other clients. | # The clients locally compute XOR of the random bits of other clients. |