It depends on whether you want to stay grounded in real-world physics, or if you want to spin off on flights of fancy.
If you want to stay in real-world physics, at the moment there is no reason to expect any civilization to use anything other than electromagnetic radiation for communication. Other than the low speed of light, which is a characteristic of the universe that it does not seem to allow any faster-than-light communication so it's not specially a disadvantage for EM, electromagnetic radiation basically has every characteristic you're looking for in a communications medium, and there's little reason to believe even an advanced civilization would use something orders of magnitude worse on numerous dimensions simply because maybe they can. This is for much the same reason that we could transport everything in our civilization by people carrying things around on Segways, but we don't, because why would we deliberately choose something suboptimal?
If you want to go off on flights of fancy, then anything is possible, but there's no way to say anything useful about it.
The "grounded in reality" answer is subject to change as our understanding of physics improves, but at the moment I wouldn't say there's any particular reason to expect this answer to change much. Even on the crazy fringe frontiers of real science, I am not aware of any candidates for communication any better than EM.
Most of the whacky ideas proposed as alternate methods fail by orders of magnitude vs EM. Might you be able to build a better neutrino detector than we can? Maybe, but it's still easier to build EM detectors, and EM emitters, by a lot. Gravity waves? Why on not-Earth would anyone spend the massive, massive amounts of energy required to do that, very klunkily and with very low bandwidth, when for literally a trillionth of a trillionth of a trillionth of a trillionth the energy expenditure you could use EM, and get higher bandwidth to boot and better reusability to boot? Quantum entanglement and teleportion are non-starters, because they both require a conventional channel to work at all, and the best tool for that communication is EM.
If you want to stay in real-world physics, at the moment there is no reason to expect any civilization to use anything other than electromagnetic radiation for communication. Other than the low speed of light, which is a characteristic of the universe that it does not seem to allow any faster-than-light communication so it's not specially a disadvantage for EM, electromagnetic radiation basically has every characteristic you're looking for in a communications medium, and there's little reason to believe even an advanced civilization would use something orders of magnitude worse on numerous dimensions simply because maybe they can. This is for much the same reason that we could transport everything in our civilization by people carrying things around on Segways, but we don't, because why would we deliberately choose something suboptimal?
If you want to go off on flights of fancy, then anything is possible, but there's no way to say anything useful about it.
The "grounded in reality" answer is subject to change as our understanding of physics improves, but at the moment I wouldn't say there's any particular reason to expect this answer to change much. Even on the crazy fringe frontiers of real science, I am not aware of any candidates for communication any better than EM.
Most of the whacky ideas proposed as alternate methods fail by orders of magnitude vs EM. Might you be able to build a better neutrino detector than we can? Maybe, but it's still easier to build EM detectors, and EM emitters, by a lot. Gravity waves? Why on not-Earth would anyone spend the massive, massive amounts of energy required to do that, very klunkily and with very low bandwidth, when for literally a trillionth of a trillionth of a trillionth of a trillionth the energy expenditure you could use EM, and get higher bandwidth to boot and better reusability to boot? Quantum entanglement and teleportion are non-starters, because they both require a conventional channel to work at all, and the best tool for that communication is EM.