What does simplicial mean in the context of QM?

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Discussion Overview

The discussion revolves around the meanings of "simplicial" and "non-simplicial" in the context of quantum mechanics, as well as their implications outside of this field. Participants explore definitions, relationships to classical probabilistic theories, and the geometric interpretations of these terms.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants inquire about the definitions of "simplicial" and "non-simplicial" specifically within quantum mechanics.
  • Others question the relevance of these terms in quantum mechanics and seek clarification on their meanings outside of this context.
  • A participant references a paper to provide additional context but expresses difficulty in understanding its content.
  • Another participant suggests that "simplicial" can be synonymous with "polytope," describing it as a shape with pointed vertices, and relates this to classical probabilistic theories.
  • It is noted that in classical probabilistic theories, every mixture corresponds to a unique combination of pure states, which contrasts with the representation of mixed density matrices.
  • One participant mentions the idea of quantum sets being visualized as a circle.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the definitions or implications of "simplicial" and "non-simplicial" in quantum mechanics, indicating that multiple views and uncertainties remain in the discussion.

Contextual Notes

Some participants express confusion regarding the definitions and implications of the terms, suggesting that there may be missing assumptions or dependencies on specific interpretations.

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What does simplicial and non simplicial mean in the context of quantum mechanics?
 
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Jilang said:
What does simplicial and non simplicial mean in the context of quantum mechanics?
What do they mean outside quantum mechanics and what makes you think they mean anything within quantum mechanics ?
 
Jilang said:
Thanks, but I am having some problems deciphering it. Is there a straightforward defininition?

Another word for simplicial is polytope - it's a shape with pointy points like a square or a triangle. In a classical probabilistic theory, every mixture is a unique mix of pure states. But this is not true for a mixed density matrix, which can be written in many ways as a mixture of pure density matrices.
 
Thanks. I will take that to mean of no fixed geometry.
 
Usually the quantum set is pictured as a circle.
 

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