Suppose they succeed in sending a micro craft to Alpha Centauri, how would it communicate with us?
Micro craft implies micro transmitter. How big a dish do you need to detect a light bulb at a distance of 4 light years?
--if a "light bulb" (100 watts worth of 500 nm wavelength photons, omindirectional) were to shine for 1 hour, that would be 9*10^23 photons emitted. At 4 light years away, that would yield a flux of 5*10^(-11) photons per square meter during that hour. So your "dish" would need to have radius=79.5 km to detect even a single one of those photons. However, by using a laser & telescope to shine the photons directly at our solar system, not omnidirectional, one could of course do considerably better. If your beam flared at angle 10^(-6) radians, then you'd increase the flux by a factor of 4*10^12, enabling a dish on earth to be able to receive 1 photon during that hour, with dish radius only 4 cm, i.e. an amateur telescope. Unfortunately, you'd also get a hell of a lot of other photons coming from alpha centauri's stars, which from Earth's point of view would still outshine that laser by a factor of about 10^12. If the laser instead of shining for 1 hour at 100 watts, instead somehow were to shine a 1 terawatt for 10^(-10) hours = 360 nanosec (same total energy), and the receivers knew at just what nanoseconds that was going to happen, then we could do better. Now, the stars only outshine the laser, from earth point of view, by factor 100. Therefore, with factor 100 outshining, earth observers could hope to detect the 1% brightness increase due to the laser, during those 360 nanosec, provided their "dish" had enough size to receive, say, 500 laser photons. So a mere 1 meter radius telescope on Earth, would suffice to receive 1 bit during that hour. And if we use the fact the laser were emitting 500 nm photons ONLY, while star emitting lots of colors, i.e. pipe our telescope thru a spectrograph into a photon detector, then we would do even better. Suppose the wavelength band is 500+-1 nm, receivers exclude all other wavelengths. Now, amazingly enough, that laser in earth's view actually is outshining the star by a factor of (very roughly) 10 during the right nanoseconds. So called "tabletop terawatt" chirped-pulse lasers can produce 1-picosec-long pulses with 1 terawatt power during that picosecond, at 10-Hz pulse rate, which is 10 watts. Therefore equipment available today hopefully fitting on 10 lab tables plus a telescope a few meters in diameter, plus some super-accurate atomic clocks, could transmit from alpha centauri to earth, perhaps a few 10s to 1000s of bits per hour with power supply of a few kilowatts to attain average transmission power 100 watts. This post here, is probably about 5 kilobits if compressed.