I agree, but for comparison, let's look at the laser than the NASA uses to measure the distance to the Moon. It has a pulse of 75mJ in 10ps, i.e. 7,000,000 Watts for a very short time, and they get back only a few photons. Alpha Centauri is 100,000,000 times more far away, so the signal is 1e16 times dimmer. You need a bigger laser or a lot of time just to be lucky to get a photon there.

Also, in comparison, the Sun has 3e26 Watts. That's distributed in the full spectrum, and the laser has a very narrow bandwidth. I can't find the exact number now, but from https://en.wikipedia.org/wiki/Laser_linewidth my guess is that it's 1/100000 of the energy is in the same band of the laser, that is 3e20Watts. Let's remove a few zeros to be sure, like 6 zeros, so my guess is something like 3e14Watts.

Comparing the guess of 3e14Watts of the Sun to the 7e6Watts of the laser. So it's not only difficult to see even a photon, there is a lot of noise in the background. I've measured signals like 1/100 of the noise level using a lock-in amplifier, and I think 1/1000 is possible, but 1/100.000.000 looks very difficult.

And now we must consider the quantum part, that is the interesting part of the post. If you generate a lot of pairs of entangled photons, after the trip you must match the photon that traveled with the photon you keep at home.

If you pick the right photon to compare, you theoretically get 100% of agreement, but my guess is that in a lab you will get 90% or less. After an interstellar trip, I'd be happy to get a 1% of correlation, and use a lot of redundancy and error correcting codes to fix it.

The problem is if you pick the wrong photon. You get perfect random noise. Absolutely no information. You can't fix it with redundancy. And with interstellar distances, you must generate a really huge number of photons just to be able to detect a photon in the other side of the communication.