Superdense Coding Protocol

Eve starts with two qubits in state  |00>

Eve prepares Bell state, first with Hadamard gate on first qubit: 0.707 |00> + 0.707 |10>

and then with controlled Not gate on the two qubits: 0.707 |00> + 0.707 |11>

Eve sends one qubit to Alice and another to Bob.

Alice wants to encode two classical bits to send to Bob with only her one qubit

First bit: 1    Second bit: 0

For encoding 10, the Z gate is applied: 0.707 |00> + -0.707 |11>

Because Alice and Bob's qubits were entangled by Eve,
Alice's operations affect both, despite being far apart.

Alice sends her qubit to Bob.                 If someone intercepts and measures the qubit,
Now Bob has both original qubits.             they measure |0> and |1> with equal probability,
Bob applies a reverse operation of            regardless of the bits encoded by Alice.
Eve's original operation
First a controlled Not: 0.707 |00> + -0.707 |10>
Then a Hadamard on the first qubit: |10>

Finally, Bob measures the qubits in the computational basis.
The result of Bob's measurement is (1,0), Alice's two bits.