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3

Information can't be transmitted faster-than-light using quantum teleportation protocol, because as you correctly noticed quantum teleportation involves classical communication between sender and receiver. The paper's abstract is saying about implementing quantum teleportation using a particular technology (silicon integrated optics) for the first time. ...

1

If you are interested only in the measurements of the system that comprises only 2nd and 3rd qubits, then you could compute the reduced density matrix $\rho_{23}$ on those qubits from the total density matrix $\rho_{1234}=|\psi\rangle \langle\psi|$, i.e. $$\rho_{23} = \text{Tr}_{14}(\rho_{1234})$$ Density matrix carry all information that is need to ...

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Judging from your computations, the Bell states are $$|B_{00}\rangle = |\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$$ $$|B_{10}\rangle = |\Phi^-\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle)$$ $$|B_{01}\rangle = |\Psi^+\rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)$$ |B_{11}\rangle = |\Psi^-\rangle = \frac{1}{\sqrt{2}}(|01\...

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