A qualified yes, because we're pretty sure there's no faster way to transfer information even with quantum whatever. The qualification is they might not use radio waves, but they're going to use some sort of light.
What is likely is they won't use omni-directional antennas for very long. Radiating energy in an expanding sphere is extremely wasteful, its power will diminish with the square of the distance. Instead, focused energy transmissions are much preferred. The ultimate expression is using a laser, which is great for talking to things in space, but not so great for talking to the next city over because the curvature of your planet gets in the way.
However, there's always a need for omni (or nearly omni) directional transmissions. A simple example is wifi Internet and cell phones, though even those are somewhat directed.
This is taken into account by the Drake equation in two parts. Fc is how many alien civilizations reveal their existence via signals into space, and L is how long their civilization sends detectable signals into space. Though we have little idea what those numbers are.
In the end, while SETI is looking for stray radiation, it's also hoping somebody else looks at the Earth and says "hmm, there's something fishy going on with their chemistry over there... too much methane and oxygen and it's absorbing too much red light. Let's beam them a hello!"
In the same time there are (probably hoax) reports of communication using Quantum nonlocality over short distances (this might only solve the energy problem).
This won't work. The speed of light is not just the speed of light, it is the maximum speed which information can be transmitted. This is called the no-communication theorem.
In physics, the no-communication theorem is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer.
In the example of quantum entanglement, if you and I carry two entangled particles away from each other and then observe them it is true that my observation causes your particle to also collapse to the opposite spin. However no information is conveyed. The original particle is in a superimposed state, and I cannot control which state it collapses to.
To use an analogy, suppose we each carried a special coin in a box. When you open the box, the other coin would immediately show the opposite. We travel away from each other and I look in the box. Mine says heads. When you look in your box yours will say tails. Because I cannot choose what face my coin will show, you can glean no information. You can't even tell when I looked at my coin, because as soon as you check inside your box you force the coin to manifest.
Veritasium has a more technical and better illustrated video on the subject.
A note on Space-QUEST. It is not a hoax. It was published in the International Astronomical Congress Proceedings. It's purpose is to eliminate some of the final loopholes which might allow quantum entanglement to communicate faster than light.
There is one way to settle the matter for sure: send entangled photons to two orbiting astronauts on board different spacecraft with large relative velocities. That leaves no room for hidden variable theories or any other fix because the peculiarities of special relativity allow both astronauts to claim the measurement on their photon was performed before the other.
Even when we're pretty sure about something, we still need experimental data to verify the theory.
Somebody mentioned neutrinos. They'd make a terrible interstellar communications medium. They're created by fusion which requires tremendous energies. They have almost no mass. They interact only via the weak nuclear force making them extraordinarily elusive. You'd need four light years of lead to reliably stop a neutrino. And they're spewed out by stars and supernova and even the cosmic background radiation causing a tremendous amount of interference.
And they only go at the speed of light giving them no advantage over photons.
I seriously doubt a civilization would discover how to create, control and detect neutrinos before they figured out electromagnetism. This is more than human-centric thinking. EM interacts with lots of things easily, is created and interacted with naturally, evolution has taken advantage of electricity independently many times, and is the simplest force to detect, create and manipulate.
Here's a great video on neutrinos by Sixty Symbols.
What is theoretically maybe possible is using a system of wormholes. Wormholes bend space itself and so avoid violating the speed-of-light. If a permanent wormhole could be established between two points, then it could be used to communicate. But that communication would still be using plain old light.