Distinguishing Two Experiments With Equal Density Matrices

[kof9595995]

For example, a esemble of 50% spin up and 50% spin down electrons, the other of 25% spin up,25% spin down, 25% x direction spin up and 25% x direction spin down. The density matrix is identity matrix for both(correct me if I'm wrong), is there any way to distinguish the two experimentally?

 

[DrChinese]

For example, a esemble of 50% spin up and 50% spin down electrons, the other of 25% spin up,25% spin down, 25% x direction spin up and 25% x direction spin down. The density matrix is identity matrix for both(correct me if I'm wrong), is there any way to distinguish the two experimentally?

I believe that these are fundamentally indistinguishable. I think there was a good quote around this, cannot recall who said this right now.

 

[kof9595995]

Emm..I also think so, but it just feels very peculiar...

 

[nismaratwork]

What about QM doesn't feel peculiar? :) I'll see if I can find that quote...