Abstract
In recent years quantum error correction (QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large NN theories. Specifically we examine SU(N)SU(N) matrix quantum mechanics and 3-rank tensor O(N)^3O(N)3 theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large NN analysis and do not appeal to a particular form of Hamiltonian or holography.
Highlights
Specific bounds for CTKT model A.6.1 Basic bounds A.6.2 Gram matrix bounds A.7
Specific bounds for matrix models A.7.1 Basic bounds A.7.2 Gram matrix bounds
It is true that BFSS at low energies does have a description in terms of ten-dimensional supergravity, but we do not expect bulk locality for a generic matrix quantum mechanics
Summary
A Proving the bound on recovery fidelity A.1 Notation A.2 Idea of the proof A.3 Orthogonal Procrustes problem A.4 Gram matrix bounds A.5 Finishing the proof A.6 Specific bounds for CTKT model A.6.1 Basic bounds A.6.2 Gram matrix bounds A.7 Specific bounds for matrix models A.7.1 Basic bounds A.7.2 Gram matrix bounds. A Proving the bound on recovery fidelity A.1. Specific bounds for CTKT model A.6.1 Basic bounds A.6.2 Gram matrix bounds A.7. Specific bounds for matrix models A.7.1 Basic bounds A.7.2 Gram matrix bounds. B Bounding operators in matrix models B.1. C Bounding singlet operators in CTKT model C.1. C Bounding singlet operators in CTKT model C.1 Hamiltonian and Casimirs C.2 Main argument C.3 Resolving anti-commutators
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