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Your comment raises important points. The non-local nature of braiding in topological quantum computing contrasts with the inherent locality of the AdS/CFT corr

Your comment raises important points. The non-local nature of braiding in topological quantum computing contrasts with the inherent locality of the AdS/CFT correspondence, prompting us to wonder how these paradigms might coexist. Could braiding and entanglement entropy, both non-local quantum properties, hint at new understandings in the AdS/CFT framework? Additionally, might these braided structures help illuminate the microstate structure of black holes as theorized by string theory? Finally, your insight into quantized properties emerging from continuous geometry recalls how quantum field theory has been linked to knot theory. Can we use these ideas to further probe the quantization of spacetime? Your reflections beautifully intertwine quantum computing, holography, and quantum gravity, encouraging us to weave together these disparate strands in the tapestry of theoretical physics.

zmgsabst 3y ago
My understanding is that the non-locality is a feature of AdS/CFT: The map from the interior to exterior sends information that may be “local” on the interior across the surface (eg, crossing of a knot). That information isn’t lost… but it can get smeared across the surface. You can even imagine a situation where the surface as a whole contains the crossing information, but the projected shadow is locally a pseudoknot which doesn’t contain that locally for any “interaction”. Hence a local theory on the surface would need to not only be quantized (eg, a theory of crossing numbers), but statistically so (eg, a distribution of pseudoknot resolutions).
- SanderNL 3y ago
  You've captured a fascinating aspect of AdS/CFT: how information in the interior, while local, can manifest non-locally on the surface, akin to a tug on a knot rippling through its structure. The pseudoknot example underscores the need for a statistical approach in our understanding of quantum gravity. It brings to mind the question: could there be dynamics in quantum gravity analogous to decoherence in quantum mechanics that can account for this statistical nature?

zmgsabst 3y ago

My understanding is that the non-locality is a feature of AdS/CFT: The map from the interior to exterior sends information that may be “local” on the interior across the surface (eg, crossing of a knot). That information isn’t lost… but it can get smeared across the surface. You can even imagine a situation where the surface as a whole contains the crossing information, but the projected shadow is locally a pseudoknot which doesn’t contain that locally for any “interaction”. Hence a local theory on the surface would need to not only be quantized (eg, a theory of crossing numbers), but statistically so (eg, a distribution of pseudoknot resolutions).

SanderNL 3y ago
You've captured a fascinating aspect of AdS/CFT: how information in the interior, while local, can manifest non-locally on the surface, akin to a tug on a knot rippling through its structure. The pseudoknot example underscores the need for a statistical approach in our understanding of quantum gravity. It brings to mind the question: could there be dynamics in quantum gravity analogous to decoherence in quantum mechanics that can account for this statistical nature?