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Predominantly Erroneous (Exohedron nonsense blog)

Discussion in 'Your Bijou Blogette' started by Exohedron, Dec 15, 2018.

  1. Exohedron

    Exohedron Doesn't like words

    The kind of coworker who, due to it being laundry day for him, is actually dressed better than usual.
  2. Exohedron

    Exohedron Doesn't like words

    I really wish I didn't have such awful reactions to alcohol. I don't get drunk, or even tipsy or relaxed; I go straight from drinking to headache without any of the desirable effects of alcohol.
  3. Exohedron

    Exohedron Doesn't like words

    Finally back to the paper! Had a long break since the last time since I accidentally closed the tab with the paper in it and thus lost momentum.

    Section 6.4: Factorizability and Cohomology
    Another reminder that for pure states we get actual factorizability, but for mixed states we don't.

    Section 6.4.1: Factorizabilia (I really like this title)
    Factorization of a bipartite state is equivalent to factorizability of the expectation of observables of the state.
    In the pure state case, this is usually detected via partial traces.
    Support factorizability: support equivalent to a product state. Extends to the mixed state case via computation of ranks.
    For pure states support factorizability implies factorizability, but not so in the mixed states.
    I'm pretty sure that the explanation of the counterexample is wrong. I mean, it's a counterexample, I think, but the constraint in the "factorizable iff" statement doesn't make any sense.
    Separable: convex lin comb of factorizable states. Generalization of entangled to mixed states.
    The example for non-separability just doesn't make sense at all. It's linear in the relevant parameter, which means that it's not a state most of the time. Also the paper claims that it's a "Werner state", but it's not.

    Section 6.4.2: Pure States
    Oh, the Schmidt rank is the rank of the partial trace. Okay. Things that would have been nice to know before starting this paper.
    I guess it would be way too much effort for papers to give lists of prereqs. And if this is in fact written for physicists and quantum information theorists in particular, I guess it makes sense that they would be familiar with this things already.
    Some nice proofs that the cohomology detects factorizability. Okay, I like that.
    I keep forgetting how the functional calculus works. The presentation here is a lot better than "oh we just pull out the positive-frequency bits".

    Section 6.4.3: Mixed States
    Yay obstructions!
    And as always examples. Let's see if these make more sense.
    Separable states that have nonvanishing cohomology. Bad. Cohomology detecting classical communication?

    And that's it for section 6.4. I'll try to not take so many breaks next time.

  4. Exohedron

    Exohedron Doesn't like words

    Starting to realize that my jokes about "what I have accomplished" maybe should be a little less self-deprecating, at least when they're parts of presentations at work.
  5. Exohedron

    Exohedron Doesn't like words

    Urban Dictionary's sole entry on "Scarlet Number" is surprisingly boring.
  6. Exohedron

    Exohedron Doesn't like words

    The kind of metaphysics that considers holes to be at least as ontologically real as anything else.
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