The goal of this project is to simulate the Multipartite Entanglement Verification protocol in a quantum network with N participating nodes. The choice of the verifier is fixed.
θ-protocol which is successor of xy-protocol described in this paper was implemented.
Flow diagram of protocol is shown below.
The network scenario we consider consists of a source and n parties with 1 fixed verifier(at 0 index). Source shares an n-qubit state ρ with n parties. One of the parties, a ‘Verifier’, would like to verify how close this shared state is to the ideal state and whether or not it contains GME.
Source shares an n-qubit state ρ with n parties.
Each party first recives its state from source through a QuantumChannel.
- If the party is verifier, it sends {0, π/2} to other parties including itself via ClassicalPrivateChannel and verifies for Entanglement.
- else it recives angle from verifier, measures in corresponding basis (x-basis for 0, y-basis for π/2) and sends its state Y={0, 1}.
- n s2p_qcs(Source to Party) were used for sharing n-qubit state ρ with n parties.
- n-1 v2p_ccs(Verifier to Party) were used.
- n-1 p2v_ccs(Party to Verifier) were used.
The verification protocol is then tested for the following input states:
Protocol succeeds with probability P(Honest) = 1 (always 1 in all no-loss cases)
Protocol succeeds with probability P(Dishonest) = 0.55 (for n=4, 100 testcase).
Explanation for the same is given in below image for |0> state, it can be seen that all the states are possible after applying protocol
but for GHZ state the equation always holds true $$ \bigoplus_{j} Y_{j} =\frac{1}{\pi}\ \sum_{j} \theta_{j} \hspace{5mm} \textbf{(mod 2)} $$
