Direct point to point conduits carrying fiber would reduce latency to a worst case of 21ms, but requires a fiber that doesn't melt at core temps (around 5200C).
We really need that WiFi-Neutrino spec to get approved
Is it easy to dig down to the core, apart from the temperature issues?
No. The deepest we've ever sent anything is a little over 12Km; the crust's minimum thickness is about 40Km, and the diameter of the Earth is about 12700Km.