Distinguishing Two Experiments With Equal Density Matrices

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Discussion Overview

The discussion revolves around the ability to distinguish between two ensembles of electrons that have equal density matrices. The focus is on the implications of quantum mechanics and the experimental feasibility of differentiating between these ensembles, which are described in terms of their spin configurations.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • One participant describes two ensembles: one consisting of 50% spin up and 50% spin down electrons, and the other consisting of 25% spin up, 25% spin down, 25% x direction spin up, and 25% x direction spin down, suggesting that both have an identity matrix as their density matrix.
  • Another participant agrees with the assertion that the density matrices are the same and proposes that the two ensembles are fundamentally indistinguishable, referencing a quote that they cannot recall.
  • A third participant expresses a feeling of peculiarity regarding the indistinguishability of the two ensembles.
  • A fourth participant comments on the peculiar nature of quantum mechanics in general and offers to search for the previously mentioned quote.

Areas of Agreement / Disagreement

Participants generally agree that the two ensembles are indistinguishable based on their density matrices, but there is an underlying sense of curiosity and discomfort regarding this conclusion.

Contextual Notes

The discussion does not resolve the implications of the indistinguishability or the experimental methods that could be employed to test this assertion, leaving open questions about the assumptions and definitions involved.

kof9595995
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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?
 
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kof9595995 said:
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.
 


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


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

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