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?