Reading and source map
The four opening lectures carry their own model calculations. These readings provide provenance, broader statements, and later comparisons. Reading every paper is not a prerequisite for taking the opening block.
Primary anchors
| Source | Role in the course | What the opening notes do themselves |
|---|---|---|
| Cleve, Gottesman, Lo, How to share a quantum secret, arXiv:quant-ph/9901025 | Quantum secret sharing and threshold access structures | Construct the three-qutrit code, trace every matrix unit, and give decoders |
| Harlow, TASI Lectures on the Emergence of the Bulk in AdS/CFT, arXiv:1802.01040 | Pedagogical connection between codes, bulk reconstruction, and the holographic dictionary | Prove the specific reconstruction identities; use the bulk terminology as a limited comparison |
| Witten, Notes on Some Entanglement Properties of Quantum Field Theory, arXiv:1803.04993 | States on algebras, finite modular theory, and the continuum QFT problem | Compute finite modular data, signs, a KMS correlator, and an oscillator example |
| Harlow, The Ryu-Takayanagi Formula from Quantum Error Correction, arXiv:1607.03901 | Complementary recovery, subalgebra codes, central entropy terms, and algebraic entropy | Derive explicit factor and direct-sum code identities; do not prove the general normal-form theorem |
The titles and identifiers of the four anchors were checked against the arXiv records; the modular and code discussions were inspected in the available full text. The new exposition and worked parameter choices are written for this course.
Gravitational comparisons
- Almheiri, Dong, Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, arXiv:1411.7041. Motivation for interpreting effective bulk observables through a code subspace. It is not a claim that a small finite code supplies gravitational dynamics.
- Maldacena, Eternal Black Holes in AdS, arXiv:hep-th/0106112. The later thermofield-double/black-hole comparison. An arbitrary thermal purification does not establish the hypotheses of this identification.
- Jafferis, Lewkowycz, Maldacena, Suh, Relative entropy equals bulk relative entropy, arXiv:1512.06431. A semiclassical gravitational relation. Lecture 4’s finite-code equality is exact in its defined model; the comparison must retain the gravitational paper’s regime.
Sources for later units
- Pastawski, Yoshida, Harlow, Preskill, Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence, arXiv:1503.06237. Small tensor networks and reconstruction. Entropy/cut equalities require the appropriate properties of the chosen model.
- Rehren, Algebraic Holography, arXiv:hep-th/9905179. Fixed-background wedge/double-cone correspondence; compare its scope with dynamical gravitational duality.
- Leutheusser and Liu, Emergent times in holographic duality, arXiv:2112.12156. A large- algebraic route to emergent bulk time. State, representation, and limiting assumptions are essential.
These are destinations, not assigned opening-block prerequisites. All later units are now written; the complete reading map identifies their sources and scope. The older bibliography also retains the canonical geometric and black-hole sources.
Pedagogical reference and conventions
The local AQFT course, especially its note standard and Tomita lecture, guides the separation of classroom, self-study, and research material.
The new holography notes use the same negative-imaginary-power modular convention and upper-strip KMS condition. A paper using the opposite sign must be translated explicitly. Primary sources are used for scientific claims; the AQFT notes are the reference for pedagogical depth and local convention consistency.