Quantum Information for Quantum Cats (10)

Road to Quantum Cryptography : Eavesdropper

Up to now, we just had two people in our quantum story, Alice la Hacedora and Bob el Observador. We now introduce another participant who tries to eavesdrop the quantum communication of Ablice and Bob. Yes, who else? It can only be Eve la Celosa who is the rival of Alice. We imagine Eve to be a very cable spy fully equipt with all quantum device available to Alice and Bob. She gets into the communication between them. Observe the quantum signal of Alice, and also tries to erace her trace by sending the identical quantum signal to Bob.

When Alice wants to send the series of bits to Bob, she has to specify the mode of encoding on top of the quantum signals by definitive fassion, i.e., by classical means. Namely Alice has to communicate whether he has used up-down coding or right-left coding through classical channel, phone, internet, or whatever available. Otherwise, Bob cannot reconstruct the bits and share the intended information.

But this necessity opens up the possibility of Eve eavesdropping that classical communication. Then Eve will be able to reconstruct the original bits from the quantum signals she has tapped, and also reproduce the same set of signals and send t to Bob as if they are the original quantum signal. Bob will not be able to distinguish that reproduced fake signals from the original untapped signals. Thus all the trouble Alice and Bob went through communicating quantum mechanically comes to nought, once it were to be supplemented by classical communication which appears to be the necessary supplement.
Now imagine, however, that Alice does not announce the mode of coding beforehand. Then Eve would not be able to decode the signal becuase, even with her best guess of encoding mode, she would err in 50% of the time, and as a result she would have to send the faked signal which is encoded in wrong mode in 50% of the time.

In such case, Bob would reconstruct the wrong signal that is differnt from what Alice has sent even when he has guessed her encoding mode.
If Alice and Bob communicate the original signal and reconstructed signal and compare them, they would easily find out whether there is Eve inbetween them tampering the signal or not.

So, with the ocasional checking in this manner inserted in the process of quantum signal sharing in earnest, they can detect the existence of Eve, and stop communicating.