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nLab > Latest Changes: ER = EPR

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  1.  
    • CommentRowNumber1.
    • CommentAuthorLuigi
    • CommentTimeApr 29th 2021

    separate page created

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2021
    • (edited Apr 29th 2021)

    I have added the following commentary. What do you think:

    This idea may usefully be compared – and maybe is in parts a way of turning into prose – the Ryu-Takayanagi formula (which has a more well-defined content is a theorem in a class of toy examples), which equates

    with

    For more on this see at holographic entanglement entropy.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 4th 2021

    I have further expanded (here) on the relation to the Ryu-Takayanagi formula, pointing out how the Majorana dimer code model of JGPE 19 gives a yet more concrete theorem resembling the “ER = EPR” slogan: They show that the entanglement entropy in a holographic tensor network model is encoded entirely by the underlying chord diagram, where each chord reflects two things at once:

    1. (ER) an entangled pair of qbits at their endpoints on the boundary

    2. (EPR) a geodesic through the hyperbolic bulk.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2021

    In the discussion of understanding “ER=EPR” as being about the RT-formula, I have added this remark:

    A precursor to this picture is the “bit-thread”-interpretation of entanglement entropy due to Freedman & Headrick 16 (notice the use of “EPR pair” in their Figure 4.)

    diff, v6, current

1 to 4 of 4

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