# Why can a point in anti-de Sitter space be modeled as a logical qutrit and how is its error correction done?

This isn't my area but the recent Quanta article How Space and Time Could Be a Quantum Error-Correcting Code struck me as interesting. They mention:

In their paper[1] conjecturing that holographic space-time and quantum error correction are one and the same, they described how even a simple code could be understood as a 2D hologram. It consists of three “qutrits” — particles that exist in any of three states — sitting at equidistant points around a circle. The entangled trio of qutrits encode one logical qutrit, corresponding to a single space-time point in the circle’s center. The code protects the point against the erasure of any of the three qutrits.

The rest of the article more or less makes sense, but this is one point where I got stuck.

1. It's not very clear to me why one space-time point can be modeled specifically by a logical "qutrit"? What's so special about a "qutrit" in this context? Why not a "qubit" or a general "qudit"?

2. How exactly does the entangled trio perform the error correction of the central logical qutrit?

Note that I'm not acquainted with the AdS/CFT formalism. So an exposition aimed at a general audience is preferable.

[1]: Bulk Locality and Quantum Error Correction in AdS/CFT (Almheiri et al., 2014)

• For the first question is it why one space-time point vs a spatial slice? Assigning a Hilbert space to a specific location when the actual Hilbert space is $L^2(\mathbb{R})$ using the entire space. – AHusain Jan 29 at 9:43
• @AHusain No, but that point isn't clear to me either. Why exactly are they dealing with individual spacetime points, or as you say, assigning a Hilbert space to a specific spacetime point? Could you elaborate on it in an answer? (Even a partial answer might be good for a start.) – Sanchayan Dutta Jan 29 at 11:03