Undergrad What does simplicial mean in the context of QM?

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The term "simplicial" in quantum mechanics refers to structures resembling polytopes, which are geometric shapes with distinct vertices, such as triangles or squares. In classical probabilistic theories, mixtures correspond uniquely to pure states; however, in quantum mechanics, mixed density matrices can represent multiple combinations of pure density matrices. This complexity highlights the non-fixed geometry of quantum states, often visualized as circular in representation. The discussion emphasizes the need for clarity in understanding these concepts within both quantum mechanics and classical contexts.

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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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