Quantum Teleportation? -- No-Cloning Theorem telling you it is impossible

Many people might be fascinated with the idea of teleportation. Ever wanna see an identical copy of yourself on Mars? The philosophy behind this idea is worth-thinking as well: Will the fantasy-like teleportation ever be possible? If all of your body parts are transformed, are you still the original human being, with the same soul?

Quantum teleportation present the same idea, but in a much smaller and obscure way --- it is the relocation of the quantum state of an object via the entangled resource. In a quantum mechanical world, it will be the cloning of any arbitrary state in one vector space transformed into another one.

The mathematical way to express this is using tensor products of the operators. Below, I performed a proof of the No-Cloning theorem, explaining why quantum teleportation is impossible (without destroying the original state),

Therefore, we can see that since entangle state cannot be separable (at the same time), it is impossible to clone a state into another vector space without damaging the information of the original one. This brings in the philosophy discussion just like the famous Theseus Ship question: For a complete physical system, if all the original states are successfully teleported, forming an identical system as before. However, every original states has either been destroyed or lost some information, which one is the 'real' physical system?