Editing Multipartite Entanglement Verification (section)

==Properties==
* This protocol is correct meaning that if the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is <math>b=0</math>.
* The outcome of the protocol directly depends on the trace distance between the shared state <math>|\psi\rangle</math> and the GHZ state. The output <math>b</math> is such that 
<math>
    b = \left\{
    \begin{array}{ll}
        0 & \mbox{with probability } 1 - \frac{\tau^{2}}{2} \\
        1 & \mbox{with probability } \frac{\tau^{2}}{2}
         
    \end{array}
    \right.
</math>
with 
<math>
    \tau=\min_{U}\mbox{TD}(|\phi_{0}^{n} \rangle\langle \phi_{0}^{n}|, U|\psi \rangle \langle \psi | U^{\dagger} )
</math>
and where TD is the trace distance and <math>U</math> is a quantum operation acting on <math>D</math> the subspace of dishonest parties involved in the protocol (ie a tensor product of an  unitary operator on <math>D</math> and the identity operator on the rest). This means that the further the shared state is from the GHZ state, the less likely the verifier is going to accept it conditioned on any quantum operation that the dishonest party can locally perform to get closer to the GHZ state.

* This protocol still works in the presence of photon losses.

* This protocol is secure for one round against any coalition of dishonest parties, including the source.

* This protocol is composably secure against a dishonest or noisy source