Not sure if I understand all the assumptions. Here is the gist of it. The debate is about the interpretation of quantum states |φ> (L2 norm unit vectors in a complex vector space). Is |φ> something physical or is it simply a outcome-probability-calculating method for predicting the quantum evolutions and measurement outcomes.
View 1: |φ> is real.
View 2: |φ> is just a model of our knowledge of what is real + rules for calculating prob outcomes.
Define the λ = { the physical state of a system }, i.e., that which //really// exists in the world. The question is whether:
λ = {|φ> and other stuff} (1)
or
λ = {other stuff not including |φ> } (2)
If you have (2) then |φ> was really just some mathematical track-keeping and calculation device -- it is not real: it is just something we use for calculation.
If (1) is true then the quantum state is part of the real world,
and in particular if quantum theory is complete, then λ = |φ>.
Point of view (2) says that the |φ> is not necessary to obtain the complete physical
state of the system.
The paper shows that point of view (2) is untenable.
Suppose only λs mattered for physics and (2) is true.
Suppose further that a single λ could correspond to two different quantum states
|φ0> and |φ+>.
Then an apparatus that only knows λ would get "confused" sometimes and say that impossible outcomes occurred. If you knew |φ>, you wouldn't get confused about these outcomes. Therefore, they conclude that |φ> is a necessary part of the physical description of the system.
Not sure if I understand all the assumptions. Here is the gist of it. The debate is about the interpretation of quantum states |φ> (L2 norm unit vectors in a complex vector space). Is |φ> something physical or is it simply a outcome-probability-calculating method for predicting the quantum evolutions and measurement outcomes.
View 1: |φ> is real.
View 2: |φ> is just a model of our knowledge of what is real + rules for calculating prob outcomes.
Define the λ = { the physical state of a system }, i.e., that which //really// exists in the world. The question is whether:
If you have (2) then |φ> was really just some mathematical track-keeping and calculation device -- it is not real: it is just something we use for calculation. If (1) is true then the quantum state is part of the real world, and in particular if quantum theory is complete, then λ = |φ>.Point of view (2) says that the |φ> is not necessary to obtain the complete physical state of the system.
The paper shows that point of view (2) is untenable.
Suppose only λs mattered for physics and (2) is true. Suppose further that a single λ could correspond to two different quantum states |φ0> and |φ+>. Then an apparatus that only knows λ would get "confused" sometimes and say that impossible outcomes occurred. If you knew |φ>, you wouldn't get confused about these outcomes. Therefore, they conclude that |φ> is a necessary part of the physical description of the system.
|φ> is real.