Note that FTL communication breaks the theory of relativity since FTL is equivalent to time travel (under some frames). Thus the best scientific knowledge is that tachyons, quantum entanglement and so on cannot carry information faster than the speed of light.
Since scientific theories such as the Theory of Relativity are not mathematically proven it is "plausible" that they will be disproven. However, given the many answers that assume that relativity is wrong, it is interesting to note that the existence of pseudo-telepathy is a known scientific fact and not limited to the speed of light.
The standard example is two space captains (Alice and Bob) who want to meet only if they both agree. They have the option of travelling to star system A or B. They say they want to meet, and they both receive a message saying to travel to system A. They arrive at system A, and meet.
Now they have received something information-like, because they were able to agree to meet, not limited by the speed of light. However, this doesn't break causality. They each have a 50% chance of receiving "A" regardless of what the the other captain responds, so there receiving "A" by itself gives no information about the other space captain. No information is exchanged until the captains meet, which happens slower than the speed of light.
Quantum mechanics doesn't allow the captain problem to be solved with 100% accuracy, but still much better than random chance.
Depending on the feel of your universe pseudo-telepathy might work better than actual communication. Imagine oracles spread across the galaxy with some from of pseudo-telepathy device wired into their brain. It gives a 100% scientific reason to have oracles that give cryptic statements that tell you what you need to know (but you don't know why until after), if that's your thing. There are limits to the what can be achieved by pseudo-telepathy, but the oracles may not even really know when they are just guessing. The main characters don't necessarily know the exact details, they consult the oracle and it works out (or not) as required by the plot.