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Verifiable Quantum Anonymous Transmission: Difference between revisions
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Let <math>C_\epsilon</math> be the event that the protocol does not abort and the state used for anonymous transmission is such that, no matter what operation the adversarial players do to their part, the fidelity of the state with the GHZ state is at most <math>\sqrt{1-\epsilon^2}</math>. Then, | Let <math>C_\epsilon</math> be the event that the protocol does not abort and the state used for anonymous transmission is such that, no matter what operation the adversarial players do to their part, the fidelity of the state with the GHZ state is at most <math>\sqrt{1-\epsilon^2}</math>. Then, | ||
<center> | |||
P[C_\epsilon] \leq 2^{-q} \frac{4n}{1 - \sqrt{1-\epsilon^2}} | <math>P[C_\epsilon] \leq 2^{-q} \frac{4n}{1 - \sqrt{1-\epsilon^2}}</math> | ||
</center> | |||
By doing many repetitions of the protocol, the honest players can ensure that this probability is negligible. | By doing many repetitions of the protocol, the honest players can ensure that this probability is negligible. | ||
If the state used for anonymous transmission is of fidelity at least <math>\sqrt{1-\epsilon^2}</math> with the GHZ state, | If the state used for anonymous transmission is of fidelity at least <math>\sqrt{1-\epsilon^2}</math> with the GHZ state, | ||
<center><math> | |||
P_{\text{guess}} [\mathcal{S} | C, \mathcal{S} \notin \mathcal{A} ] \leq \frac{1}{n-t} + \epsilon | P_{\text{guess}} [\mathcal{S} | C, \mathcal{S} \notin \mathcal{A} ] \leq \frac{1}{n-t} + \epsilon | ||
P_{\text{guess}} [\mathcal{R} | C, \mathcal{S} \notin \mathcal{A} ] \leq \frac{1}{n-t} + \epsilon | </math></center> | ||
<center><math> | |||
P_{\text{guess}} [\mathcal{R} | C, \mathcal{S} \notin \mathcal{A} ] \leq \frac{1}{n-t} + \epsilon | |||
</math></center> | |||
where <math>\mathcal{A}</math> is the subset of <math>t</math> adversaries among <math>n</math> nodes and <math>C</math> is the register that contains all classical and quantum side information accessible to the adversaries. | where <math>\mathcal{A}</math> is the subset of <math>t</math> adversaries among <math>n</math> nodes and <math>C</math> is the register that contains all classical and quantum side information accessible to the adversaries. | ||