Simulating Multipartite Entanglement Verification Protocol using NetSquid

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.

Approach

θ-protocol which is successor of xy-protocol described in this paper was implemented.

Flow diagram of protocol is shown below.

Implementation

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.

Protocols

SourceProtocol

Source shares an n-qubit state ρ with n parties.

PartyProtocol

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}.

Channels

Quantum Channels

• n s2p_qcs(Source to Party) were used for sharing n-qubit state ρ with n parties.

Classical Channels

• n-1 v2p_ccs(Verifier to Party) were used.
• n-1 p2v_ccs(Party to Verifier) were used.

Result

The verification protocol is then tested for the following input states:

• The input state is the N-partite GHZ state.

Protocol succeeds with probability P(Honest) = 1 (always 1 in all no-loss cases)

• The input state is |0> on all N-qubits.

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 $$ \bigoplus_{j} Y_{j} =\frac{1}{\pi}\ \sum_{j} \theta_{j} \hspace{5mm} \textbf{(mod 2)} $$