I seem to be at a loss to understand something pertaining to the role of the phase factors in defining quantum states and their consequences in quantum computing. So, I learnt in class and read in numerous books, and online, that the phase factor has no physical significance as it does not affect the expectation value. However, I've also heard of holonomic quantum computation, which uses phase changes to perform logic operations and store data. This seems a little confusing to me, as the information operated on in the operation will eventually need to be read out. But how can one see the affect of the logic gate in a measurement if the phase change has no physical effect, i.e. how can one distinguish between a prepared state that has gone through a phase changing gate and one that hasn't? And can't these phase changes be observed in interference experiments which would imply they have some physical significance? Also, the density matrix description of states does not include a phase term but I also know that these matrices are used in describing quantum information processes but I'm unsure how without the phase information? I'm sure I'm just missing some aspect to link all of this together, could anyone point me the right way?