Wondering about quantum information and phase factors.

[Beer-monster]

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 learned 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?

 

[Beer-monster]

Let me try to work through this a bit more.

So after some reading I found out that I wasn't being specific enough. It's global phases differences that have no physical significance, but relative phases do. Operations that shift the relative phase do affect the state as represented by rotations of the state vector on the Bloch sphere.

Following this logic, in interference experiments when the shifted and unshifted states meet they form a superposed state with a relative phase shift, which affects the resulting measured.

As the global phase factor makes no difference, the fact that this is lost when computing density matrices does not effect its use in describing quantum information.

Does this sound something like correct? Any guidance would be appreciated.

 

[Joseph14]

Sounds good to me. I'm learning Quantum Information right now too, so I'm not an expert, but it looks like you've answered your question.