# Why are the equal probabilities for Bell state measurement outcomes essential for “quantum teleportation”?

I've recently been introduced to the basics of finite-dimensional quantum mechanics from a purely mathematical point of view (with a quantum-information theme to it). When discussing quantum teleportation, the professor made a remark about how the fact that the probability of each Bell state measurement outcome is 1/4 independently of the measured state is fundamental for the protocol to work.

However, I fail to see what the mathematical reason for this is. Is there an easy explanation for this fact?

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