Non-trivial area operators require non-local magic
Open accessAbstract
A bstract: We show that no stabilizer codes over any local dimension can support a non-trivial area operator for any bipartition of the physical degrees of freedom even if certain code subalgebras contain non-trivial centers. This conclusion also extends to more general quantum codes whose logical operators satisfy certain factorization properties, including any complementary code that encodes qubits and supports transversal logical gates that form a nice unitary basis. These results support the observation that some desirable conditions for fault tolerance are in tension with emergent gravity and suggest that non-local “magic” would play an important role in reproducing features of gravitational back-reaction and the quantum extremal surface formula. We comment on conditions needed to circumvent the no-go result and examine some simple instances of non-stabilizer codes that do have non-trivial area operators.
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Previous works have shown strong limitations for nontrivial area operators emerging from stabilizer codes and holographic codes in the presence of symmetry.
“Previous works have shown strong limitations for nontrivial area operators emerging from stabilizer codes [10] and holographic codes in the presence of symmetry.”
From Hyperinvariant spin network states — an AdS/CFT model from first principles (2026) · cites this paper as [10]
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References 55 · Cited by 17
- Authors
- Cao, C.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Cao, ChunJun
- ORCID
- Cao, ChunJun
- Venue
- Journal of High Energy Physics
- Published
- 2024-11-19
- Volume
- 2024
- Issue
- 11
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W4404574771
- Cited by
- 17
- References
- 55
- Citations by year
- 2026: 9 · 2025: 7 · 2023: 1
- FWCI
- 1.14
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Locations
- Journal of High Energy Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion, cc-by)
- VTechWorks (Virginia Tech) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Funders
- National Science Foundation (1733907)
- Institute for Quantum Information and Matter, California Institute of Technology (PHY-1733907)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- area operator, stabilizer codes, quantum error-correcting codes, complementary codes, fault tolerance, emergent gravity, quantum extremal surfaces
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