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Not quite the minimum. :-)

Beams of neutrinos can be sent through the Earth and detected on the other side.

This is true. Using a neutrino beam, the minimum latency would be approximately:

(diameter of Earth) / (speed of light) ~= 42.5 milliseconds

Some high-frequency traders might actually be able to justify the investment needed to enable such low-latency communications!

Come to think of it, you could also use gravitational waves...