Undergrad QKD Question: Alice & Bob Detector Cross-Checking

[Madi Araly]

Hello,

I've been learning about Quantum Key Distribution recently, but I can't seem to find the logic in one of the steps... maybe I'm just having a brain block.

So let's say Alice has sent a stream of entangled photons to Bob, and he finishes measuring them and is left with a binary code. All of the lessons I've watched tell me that Alice will tell him "right" or "wrong" once he states which detector he used for each one, but where is this communication supposed to take place?

It doesn't occur in the same system through which the photons were sent, but I don't see how they could do this over any system that Eve could not access. They could meet in person, but arrangements like this would be too impractical in almost all cases. Any insight?

 

[jfizzix]

That's the thing. Eve does have access to Bob's message to Alice about what basis he measured in for each pair of photons, but that info doesn't help her learn about Alice and Bob's secret key.

The way I understand it is that Bob tells Alice what basis he measured in after he measures his photon. If Eve intercepted the photon en route to Bob, she has a 50/50 chance of measuring in the same basis that Bob chooses.

When Bob and Alice have finished their measurements, they can take a random subset of them, and actually compare outcomes publically. These bits won't be used for the secret key, but can be used to test the security of the quantum channel. If Eve were intercepting photons, measuring them, and sending them on their way, then instead of having nearly 100 percent correlation when Alice and Bob measure in the same basis, the correlation will be much lower. If their measured correlation is high enough, they know with high probability that Eve couldn't be listening in, and they key they share is secure.

After that, Alice and Bob's keys are not necessarily identical, due to experimental noise and such, but they can perform information reconciliation to get a smaller identical key, and privacy amplification to get an even smaller secret key about which Eve can know nothing (in the sense that Eve would be equally likely to guess all possible keys with her info).

 

[Madi Araly]

That's the thing. Eve does have access to Bob's message to Alice about what basis he measured in for each pair of photons, but that info doesn't help her learn about Alice and Bob's secret key.

The way I understand it is that Bob tells Alice what basis he measured in after he measures his photon. If Eve intercepted the photon en route to Bob, she has a 50/50 chance of measuring in the same basis that Bob chooses.

When Bob and Alice have finished their measurements, they can take a random subset of them, and actually compare outcomes publically. These bits won't be used for the secret key, but can be used to test the security of the quantum channel. If Eve were intercepting photons, measuring them, and sending them on their way, then instead of having nearly 100 percent correlation when Alice and Bob measure in the same basis, the correlation will be much lower. If their measured correlation is high enough, they know with high probability that Eve couldn't be listening in, and they key they share is secure.

After that, Alice and Bob's keys are not necessarily identical, due to experimental noise and such, but they can perform information reconciliation to get a smaller identical key, and privacy amplification to get an even smaller secret key about which Eve can know nothing (in the sense that Eve would be equally likely to guess all possible keys with her info).

Ahh, I get it now. You managed to explain it in a better way than many of the lectures, so hats off to you. Thanks for your help!