I am a Physics Teacher at pre university level.
Tunneling, wavefunctions and uncertainty are on the syllabus on a very vague way. Quantum superposition and entanglement are not but tie in well and I think can be thought of in a macroscopic way that helps people grasp how odd quantum really is.
So I thought. I should make a quantum circuit on IBM Q experience that "proves" quantum entanglement and superposition. The standard tutorial has a structure like this.
H . Z + Z
Which uses a Haddard Z to make a superposition and a CNOT + to entangle the qbits. The quantum superposition collapses at the first measurement Z giving a random output (which is "transmitted" to the entangled qbit and therefore it has the same state)
The results are as expected. Both gates give the same value when measured (00) or (11).
BUT this system gives the same results as if the Haddard gate just randomly selected a state and the CNOT was an Xor
So I do TRUST the website from IBM which tells me it was an entangled superposition (Mostly) but how can I convince my students that the randomness happened at the Z, not the H.
Is there a simple circuit which shows that the qbits really are entangled?
Maybe I can put a gate in which affects one qbit and show that it affected the other This fits with the idea you need to put a circuit inside the circuit and the external circuit can tell you some properties of the internal circuit. This seems to be how the circuit above is "useful", to tell if the circuit flips only one bit.
In that case the simplest possible example is...
H . Z X NOT Z
Which still gives the expected results from a classical system.
Maybe that didn't work because the quantum system follows classical rules REALLY closely (which does seem to fit). In this case you can only show a system is quantum buy solving problems that only a quantum computer could solve. i.e. we cannot be sure (without external knowledge of other experiments) that the quantum computer is actually quantum until/unless supremacy is achieved.
Help, my brain hurts.