Sandwiched Renyi Relative Entropy in AdS/CFT
- URL: http://arxiv.org/abs/2204.07694v1
- Date: Sat, 16 Apr 2022 01:13:29 GMT
- Title: Sandwiched Renyi Relative Entropy in AdS/CFT
- Authors: Reginald J. Caginalp
- Abstract summary: We explore the role of sandwiched Renyi relative entropy in AdS/CFT and in finite-dimensional models of holographic quantum error correction.
In particular, we discuss a suitable generalization of sandwiched Renyi relative entropy over finite-dimensional von Neumann algebras.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We explore the role of sandwiched Renyi relative entropy in AdS/CFT and in
finite-dimensional models of holographic quantum error correction. In
particular, in the context of operator algebra quantum error correction, we
discuss a suitable generalization of sandwiched Renyi relative entropy over
finite-dimensional von Neumann algebras. It is then shown that the equality of
bulk and boundary sandwiched relative Renyi entropies is equivalent to
algebraic encoding of bulk and boundary states, the Ryu-Takayanagi formula, the
equality of bulk and boundary relative entropy, and subregion duality. This
adds another item to an equivalence theorem between the last four items
established in arxiv:1607.03901. We then discuss the sandwiched Renyi relative
entropy defined in terms of modular operators, and show that this becomes the
definition naturally suited to the finite-dimensional models of holographic
quantum error correction. Finally, we explore some numerical calculations of
sandwiched Renyi relative entropies for a simple holographic random tensor
network in order to obtain a better understanding of corrections to the exact
equality of bulk and boundary sandwiched relative Renyi entropy.
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