To add: I think the other use of “pure state” comes from this context. Here if you have a system of commuting operators and take a joint eigenspace, the projector is mixed, but it is pure if the joint eigenvalue uniquely determines a 1D subspace; and then I think this terminology gets used for wave functions as well
Thanks—you’re right. I have seen “pure state” referring to a basis vector (e.g. in quantum computation), but in QTD your definition is definitely correct. I don’t like the term “pointer variable”—is there a different notation you like?
I’d prefer “basis we just so happen to be measuring in”. Or “measurement basis” for short.
You could use “pointer variable”, but this would commit you to writing several more paragraphs to unpack what it means (which I encourage you to do, maybe in a later post).
Your use of “pure state” is totally different to the standard definition (namely rank(rho)=1). I suggest using a different term.
To add: I think the other use of “pure state” comes from this context. Here if you have a system of commuting operators and take a joint eigenspace, the projector is mixed, but it is pure if the joint eigenvalue uniquely determines a 1D subspace; and then I think this terminology gets used for wave functions as well
Thanks—you’re right. I have seen “pure state” referring to a basis vector (e.g. in quantum computation), but in QTD your definition is definitely correct. I don’t like the term “pointer variable”—is there a different notation you like?
I’d prefer “basis we just so happen to be measuring in”. Or “measurement basis” for short.
You could use “pointer variable”, but this would commit you to writing several more paragraphs to unpack what it means (which I encourage you to do, maybe in a later post).