Sending spacecraft over interstellar distances (as proposed by the Breakthrough Starshot project) is difficult enough, but assuming your tiny (single digit gram) probe gets there, how does it “phone home” to tell you what it found? Maxwell’s equations set upper limits on what you can accomplish in electromagnetic propagation regardless of how clever you are, and fundamentally, “there’s no substitute for aperture and power”, both of which are in short supply in a tiny probe. It would be more than disappointing to spend 20 to 30 years getting to Proxima Centauri and then have the pictures come back at something like one bit per second.
How might this challenge be met, and what are the fundamental limits on communication with interstellar craft?
According to orthodox quantum mechanics there is no way to use entangled particle pairs to send signals faster than light. While entanglement causes measurements made on particles at an arbitrary distance to be correlated (if Alice measures spin-up, Bob will always measure spin-down, for example), the individual measurements are random, so there is no way for Bob to decode the message unless Alice’s measurements are sent to him by classical means, which is never faster than light. Here is a popular article from Forbes which explains this in more detail.
There are theoretical extensions to quantum mechanics (sometimes called “post-quantum theories”) which might permit faster than light signaling, but there is, at present, no experimental evidence for these theories. Here is an article by Stephen Wolfram on how his emerging fundamental theory might permit faster than light signaling.
Any means of faster than light communication would, of course, allow one to build an antitelephone or ansible, which would violate the principle of causality. But maybe causality is just something we observe at a large scale, like thermodynamics, and not built in at a fundamental level.