Deconfinement and error thresholds in holography

We study the error threshold properties of holographic quantum error-correcting codes. We demonstrate that holographic conformal field theories admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the Hawking-Page phase transition to motivate the conformal field theory result, and comment on potential extensions to other confining theories.

Figure 1

A holographic subsystem code whose boundary sites are coupled to an external system that introduces thermal noise locally. Logical information is stored at region $A$ where as the remaining bulk regions belong to $B$. The spatial slice has hyperbolic geometry. Colored regions known as entanglement wedges are bounded by the boundary anchored geodesics and the disjoint boundary intervals.

Figure 2

Circuit illustration of the scenario of the code-capacity threshold. One applies a single-shot thermal noise and then applies the decoding and recovery operations to recover the locally corrupted quantum information.

Figure 3

(a) Boundary probes scatter off of an encoded qubit in the center of AdS when the background is (thermal) AdS. (b) The same boundary probes will only yield scrambled information from the black hole, and only effectively after the Page time of the black hole, where the logical information cannot be reliably accessed.