dmitry | Jan. 4, 2021, 11:53 a.m.
Continuing on with the CERN video lecture series, this post covers the second lecture in their series.
Another way of representing a qubit is by using the Bloch sphere (where qubit states of fully 0 or fully 1 are on opposite poles akin to the north and south poles), which opens the potential for rotation gates, which can be represented as rotating the position of the qubits on the sphere (or rotate the sphere while keeping one axis fixed).
The lecture then switches to a practical discussion of how quantum computing can impact information exchange over an insecure channel. Classically, this could be done by using one-time pads that are preshared to encrypt and decrypt the data (by exclusive or). The challenge is how do we keep presharing these pads that cannot be reused to preserve perfect secrecy (which can be quite long as they need to be as long as the message to be encrypted)? So far we have used classical key distribution methods such as the Diffie-Helman protocol or public key cryptography, but these rely on hardness assumptions that hold true for classical computers (i.e. finding math problems that are very hard and take an absurdly long amount of time for classical computers to do and using them within those protocols) and do not hold true for quantum computers (this is where the CERN lectures intersects with Simon Singh's book!).
BB84 was the first protocol for quantum key distribution. This is done by Alice generating a private string of random qubits and then randomly choosing to encode the qubits in the |0>,|1> basis (vertical/horizontal) or the |+>, |-> basis (where |+> = 1/sqrt2(|0> + |1>) and |-> = 1/sqrt(|0 - |1>) (diagonal basis) before then sending them to Bob over a quantum channel. Each time Bob receives a qubit, he randomly decides whether he will measure the qubit in the |0>,|1> basis or the |+>, |-> basis by applying the H gate (if he gets |0>, he writes down a 0, if a |1> then 1, if |+> then 0, if |-> then 1). After all the qubits have been measured, both Bob and Alice communicate the bases they used to code and decode the bits over an insecure classical channel (Bob does not announce his results and he discards the bits that were not measured on the same basis as Alice's picks, leaving around half of the original qubits). Attempts by men in the middle to alter the string is detected since the malicious party has no way of knowing what basis was chosen by Alice.
When working with a system of two qubits, the CNOT gate is used to leave the first qubit unchanged and flip the second qubit. There us no quantum gate that makes copies of an unknown qubit. An interesting concept in a system of multiple qubits is that of entangled states, which are states that are not the product of two independent qubits (if the first qubit is a 0, then the second one will also be a 0).
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