Quantum Key Distribution - interception confusion

[JaneHall89]

I'm battled by my thought of interception.

The entangled photon between Alice and Bob, suppose the one at Alice's side is already measured to be 1, so the second is heading over to Bob to be 0. Eve gets to it first and measures it to be 0.

Knowing its 0, eve prepares a photon of state 0 and sends it to Bob.

Both Alice and Bob are oblivious to the interception. What am I missing ?

 

[DrClaude]

Eve doesn't know which polarization Alice used for the detection. If she didn't use the same polarization as Alice while Bob did, there is a great risk she will be noticed.

See https://en.wikipedia.org/wiki/Quantum_key_distribution#Intercept_and_resend