I am interested to know if models in quantum mechanics and techniques like superdense coding teleportation are just single cases where they were found to work. Or rather just a prototype of many other examples of similar things.

What I mean is, the Deutsch oracle is just a single algorithm that was found or they found many examples similar to this and it is just a prototype?

Superdense works only if you follow the exact protocol of applying $\Bbb I$, $X$, $Z$, $ZX$? Only two qubits? Or rather it's just an example of many other known things? It seems unreasonable that this is a single example. Aren't there other 3, 4 qubits with same techniques performed by applying other matrices?

Same for teleportation.


As for superdense coding, you can design different schemes for $n, m$ qubits, but they are not giving any advantage over a simple scheme $1 \text{qubit} + 1 \text{ebit} \rightarrow 2 \text{cbits}$. In general, if Alice has access to $n$ qubits and Bob has access to $m$ qubits and all $n+m$ qubits are entangled, then Alice can't transmit more than $n+\text{min}(n,m)$ classical bits by sending her qubits to Bob.

You can, of course, change the task. For example, there can be many parties instead of just two, or your task might be to transmit qubits with a lesser amount of qubits by consuming entangled qubits, etc. Those tasks have different answers and different optimal schemes.


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