Why is it necessary for all the component-states to have same phase for interference?

I am currently reading Decoherence. In this site, it is written :

Now here is the absolutely key point: every component eigenstate has an associated phase . It is this phase$^1$ which gives the wavefunction its "wavelike" character (in complex space, remember). In order for the components to combine together correctly to produce a superposition state, they must be in the same phase (must be coherent). This is what happens in the double-slit experiment: interference components possessing the same phase combine to produce the interference effects.

$^1$What phase is he talking about? Why is it necessary for each component to be in the same "phase"?

What happens to a quantum particle in the real world is that each of its component states gets entangled (separately) with different aspects of its environment. As seen in the page on Quantum Entanglement, when particles become entangled you have to consider them as one single, entangled state (you use the tensor product to calculate the resultant state). So each component of our quantum particle forms separate entangled states. The phases of these states will be altered. This destroys the coherent phase relationships between the components.

Why does the phase relationship get altered after entanglement?

• When you do a double slit experiment the phase relationships between the interfering source are set by the geometry of the slits. This is called "spatial coherence" and it's probably better if you get used to the concept in classical wave optics, first, where all the conceptual complications due to quantum mechanics are gone. I am not all that sure that the site you picked is that great at explaining decoherence, though. It basically appeals to your ability to make analogies to things that it assumes you know already... which in this case is not a good idea. – CuriousOne Jun 28 '15 at 6:39
• Why do you think that site is a credible/good source at all? Also, you should not jump into decoherence/the measurement problem until you have firmly grasped all the concepts of quantum mechanics outside of it. – ACuriousMind Jun 28 '15 at 9:36