Quantum error correction as an organizing principle for spacetime — and the entanglement structures, codes, and operator algebras that make it work.
Holographic codes can protect bulk information even when the boundary is erased in a fractal pattern, an effect called uberholography. No-go theorems rule this out for topological codes on fractals in two dimensions. With Ning Bao, I showed that a Sierpinski-triangle boundary region in AdS4/CFT3 keeps these code properties, with a code-distance exponent of log 3 / log 4, while the Sierpinski gasket in AdS5/CFT4 does not. We then showed that the codes survive highly entropic mixed states in the bulk, whose effect is suppressed exponentially in the fractal level.
With Abhik Bhattacharjee, I checked these results against black-hole backgrounds, extended them to strips in higher dimensions, where the code properties hold only asymptotically, and related uberholography to one-shot holography and complexity transfer.
Which combination of entropies, or of optimized quantities like the entanglement of purification, detects a given kind of multipartite correlation? The tripartite signal I defined with Ning Bao and Keiichiro Furuya works for any finite-dimensional quantum state: it is non-negative, vanishes on product states and is blind to GHZ-type entanglement. Its holographic version and a mixed-state extension of the holographic signal inequality are described on the Holography page.
Topological entanglement entropy detects topological order in gapped ground states through subtraction schemes, such as those of Kitaev–Preskill and Levin–Wen. With Sai Satyam Samal, I stated conditions under which a combination of entropies captures the topological term, which places those two schemes in different classes, and showed that the facet holographic entropy inequalities are satisfied by nondegenerate ground states of topologically ordered two-dimensional media.
I am currently thinking about how quantum information can be used to bootstrap physical theories.
My first papers were on quantum game theory. I pointed out that a published quantization of the Colonel Blotto game does not reduce to the classical game when every player uses classical strategies. With Alan Maioli, I then built a multiplayer quantum Blotto game in which each player has their own qubit, which restores the classical limit and gives players with quantum strategies an advantage. The published version includes an all-optical experiment with José Huguenin's group at Universidade Federal Fluminense.
How these papers connect to each other, and to my other work: My Research Journey.