BB84

Suppose Alice and Bob have one classical communication channel and one quantum.
Eve is able to listen in to both of them.
Alice wants to sent a private message to Bob.
This algorithm is only concerned with them generating
a SHARED SECRET KEY.
Sending the message will be easy later.

Step 1

Alice generates 2 -bit strings uniformly at random

and prepares an -qubit state

• If then she encodes in
  So and
• If then she encodes in
  So and
  Alice sends to Bob through uses of the qubit channel

Step 2

Suppose there was no tampering and no noise in what Bob receives.
He generates a new -bit string uniformly at random

• If then he measures the th qubit in
• If then he measures the th qubit in
  Let be the outcome of the measurement in each case (in case of and it is 0 and 1 respectively)

Now if then

Step 3

Alice and Bob compare over the public classical channel and
They discard all the and for which
They do not reveal the other and
They are left with shorter strings and
IF there was no tampering, then and this is THE SHARED SECRET KEY.
On average there will be bits left.

Step 4

Alice and Bob first find the bit error rate in .
To do this, they take a sample
and publicly compare it to determine the bit error rate.
They discard all of those bits that are used.
They assume the rest of the strings have the same BER.
They correct the errors via Information Reconciliation (tbd)
This leaks some info to Eve. but it ok trust me.

Step 5

Privacy Amplification
From the estimated BER, they can infer how much information Eve has about the final strings.