1         Classical random vector / Classical probability & Quantum probability

1.1   From coin-flip random vector to probabilistic quantum state, it is a good educational way to

• help students to learn, from 1-norm to 2-norm

• learn entropy also exists in probabilistic classical world

• learn transformation matrix in linear classical world and quantum world

1.2   Quantum probability programming assignment

1.2.1       How ry (and x) works for single-qubit system

The following geometric picture intuitively explains one of the ways to make 

1.2.2       How to generate Bell vector via Hadamard and CNOT for 2-qubit system

You may be first troubled by the gramma of Python, but experienced programmer may help.  The last exercise of the first assignments requires students to spent effort in studying IBM qiskit manual, in order to find out how a Hadamard gate may generate a  Bell vector via CNOT gate, and using Python programming, the Bell vector will get you 

So, I reviewed what I learned from a Quantum computing textbook and brought it to church on Sunday，searching diligently a transformation method when my wife went to teach Sunday school, but in vain.  Afterwards, we went home and had a nap.  In a nap dream，I discover I can use sine/cosine right-angle transformation.  After waking up，I tried rotation（rx, ry, rz）transformation. Accidentally I saw z-transformation is the way to go.  

1.3   Teleportation瞬移

I never fully understand things about Alice and Bob when I study Bell vector.  I cannot say I understand it now, but from Nielson’ textbook, the communication between Bob and Alice still needs a classical channel to fulfill in addition to teleportation of quantum entanglement. Therefore, the claim of super-light speed never holds.  At any rate, it is new to me that entanglement communication (teleportation) has such limitation.  This reduces my faith somewhat on quantum communication.