added some qkd qworld course notes

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courses/qworld/qclass23-24/qkd/notes-2-BB84.md

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+## No cloning theorem
+* You can't copy a state if you don't know the $\alpha$ and $\beta$ values
+
+
+## Measurements
+* you create something in the $Z$ basis, then You measure in the $X$ basis, you have 50% of chance of not getting the initial prepared state
+
+## QKD
+1. Alice create a sequence of zeros and ones
+2. Alice selects a random basis for each bit to be encoded
+3. Alice sends the resulting states for Bob
+4. Bob pick random basis to try to decode what Alice has sent
+5. Alice publishes (publicly) the basis that she's used
+6. they discard the values that bob measured with the wrong basis
+
+* after the QKD, the final key Will be roughly 50% of the inital one
+
+
+* If Eve tries to measure the values in a man-in-the-middle attack, it'll cause disturbance in the Bob's measured values, so the error rate in the system may increase
+* If Eve attacks, It may not know the whole key, just about 50% of it
+
+## BB84
+* the used basis are non orthogonal one to another
+
+* Hemogenization(random permutation): we distribute equally the disturbance through the whole key, so we know how much disturbance we expect to have in the Bob results.
+	* If the final disturbance(QBER, quantum bits error rate) is <= the expected, we just apply a error correction code and a privacy amplification algorithm (these are classical)
+	* However, if the QBER is high, we abort the protocol
+
+## Six-state protocol
+* You add more basis that a qubit can be measure, this decreases the amount percent of the key that Eve can have during a attack
+* it also shrinkins the length of the key by $1\over N$ where $N$ is the number of basis
+
+## Entanglement QKD
+* Randomness: it's good because you can create random states just by measuring a quantum satte that are in entanglement
+* monogamy: If a state is maximally entangled, it's totally unentangled with other parts, so if Alice and Bob are maximally entangled there's noone attacking the communication
+* Whole vs part: You have a qubit in $Z$ basis that came from a entangled state, you can't know from what state it came from
+
+* to check if Alice and bob are maximally entangled, we can Use the CHSH inequality, then if the get the expectation value of the system as $< C > = 2 \sqrt{2}$, so Eve isn't there