@article{LiebRuskai1973,
  author = {Lieb, Elliott H. and Ruskai, Mary Beth},
  title = {Proof of the strong subadditivity of quantum-mechanical entropy},
  journal = {Journal of Mathematical Physics},
  volume = {14},
  number = {12},
  pages = {1938--1941},
  year = {1973},
  doi = {10.1063/1.1666274}
}

@book{EtingofEtAl2011,
  author = {Etingof, Pavel and Golberg, Oleg and Hensel, Sebastian and Liu, Tiankai and Schwendner, Alex and Vaintrob, Dmitry and Yudovina, Elena},
  title = {Introduction to Representation Theory},
  series = {Student Mathematical Library},
  volume = {59},
  publisher = {American Mathematical Society},
  year = {2011},
  url = {https://math.mit.edu/~etingof/reprbook.pdf}
}

@article{NachtergaeleOgataSims2006,
  author = {Nachtergaele, Bruno and Ogata, Yoshiko and Sims, Robert},
  title = {Propagation of Correlations in Quantum Lattice Systems},
  journal = {Journal of Statistical Physics},
  volume = {124},
  pages = {1--13},
  year = {2006},
  doi = {10.1007/s10955-006-9143-6},
  eprint = {math-ph/0603064},
  archivePrefix = {arXiv}
}

@article{NachtergaeleSims2006,
  author = {Nachtergaele, Bruno and Sims, Robert},
  title = {{Lieb--Robinson} Bounds and the Exponential Clustering Theorem},
  journal = {Communications in Mathematical Physics},
  volume = {265},
  pages = {119--130},
  year = {2006},
  doi = {10.1007/s00220-006-1556-1},
  eprint = {math-ph/0506030},
  archivePrefix = {arXiv}
}

@article{Winter2016,
  author = {Winter, Andreas},
  title = {Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints},
  journal = {Communications in Mathematical Physics},
  volume = {347},
  number = {1},
  pages = {291--313},
  year = {2016},
  doi = {10.1007/s00220-016-2609-8},
  eprint = {1507.07775},
  archivePrefix = {arXiv}
}

@article{ChristandlEtAl2007,
  author = {Christandl, Matthias and K{\"o}nig, Robert and Mitchison, Graeme and Renner, Renato},
  title = {One-and-a-half quantum {de Finetti} theorems},
  journal = {Communications in Mathematical Physics},
  volume = {273},
  number = {2},
  pages = {473--498},
  year = {2007},
  doi = {10.1007/s00220-007-0189-3},
  eprint = {quant-ph/0602130},
  archivePrefix = {arXiv}
}

@article{CarlenVershynina2019,
  author = {Carlen, Eric A. and Vershynina, Anna},
  title = {Recovery map stability for the data processing inequality},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {53}, number = {3}, pages = {035204}, year = {2020},
  doi = {10.1088/1751-8121/ab5ab7},
  eprint = {1710.02409}, archivePrefix = {arXiv},
  note = {The cited Lemma 2.1 is located in arXiv:1710.02409v3}
}

@article{Hastings2007,
  author = {Hastings, M. B.},
  title = {An Area Law for One Dimensional Quantum Systems},
  journal = {Journal of Statistical Mechanics: Theory and Experiment},
  volume = {2007},
  pages = {P08024},
  year = {2007},
  doi = {10.1088/1742-5468/2007/08/P08024},
  eprint = {0705.2024},
  archivePrefix = {arXiv}
}

@article{CramerEisertPlenioDreissig2006,
  author = {Cramer, M. and Eisert, J. and Plenio, M. B. and Drei{\ss}ig, J.},
  title = {Entanglement-area law for general bosonic harmonic lattice systems},
  journal = {Physical Review A},
  volume = {73},
  number = {1},
  pages = {012309},
  year = {2006},
  month = jan,
  doi = {10.1103/PhysRevA.73.012309},
  eprint = {quant-ph/0505092},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1103/PhysRevA.73.012309}
}

@article{BrandaoHorodecki2015,
  author = {Brand{\~a}o, Fernando G. S. L. and Horodecki, Micha{\l}},
  title = {Exponential Decay of Correlations Implies Area Law},
  journal = {Communications in Mathematical Physics},
  volume = {333},
  pages = {761--798},
  year = {2015},
  doi = {10.1007/s00220-014-2213-8},
  eprint = {1206.2947},
  archivePrefix = {arXiv}
}

@article{AnshuAradGosset2022Subvolume,
  author = {Anshu, Anurag and Arad, Itai and Gosset, David},
  title = {Entanglement Subvolume Law for {2D} Frustration-Free Spin Systems},
  journal = {Communications in Mathematical Physics},
  volume = {393},
  pages = {955--988},
  year = {2022},
  doi = {10.1007/s00220-022-04381-2},
  eprint = {1905.11337},
  archivePrefix = {arXiv}
}

@inproceedings{AnshuAradGosset2022Area,
  author = {Anshu, Anurag and Arad, Itai and Gosset, David},
  title = {An area law for {2D} frustration-free spin systems},
  booktitle = {Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing},
  pages = {12--18},
  year = {2022},
  doi = {10.1145/3519935.3519962},
  eprint = {2103.02492},
  archivePrefix = {arXiv}
}


@article{Kitaev2006Anyons,
  author = {Kitaev, Alexei},
  title = {Anyons in an exactly solved model and beyond},
  journal = {Annals of Physics},
  volume = {321},
  number = {1},
  pages = {2--111},
  year = {2006},
  doi = {10.1016/j.aop.2005.10.005},
  eprint = {cond-mat/0506438},
  archivePrefix = {arXiv}
}

@article{SwingleMcGreevy2016,
  author = {Swingle, Brian and McGreevy, John},
  title = {Renormalization group constructions of topological quantum liquids and beyond},
  journal = {Physical Review B},
  volume = {93},
  pages = {045127},
  year = {2016},
  doi = {10.1103/PhysRevB.93.045127},
  eprint = {1407.8203},
  archivePrefix = {arXiv}
}

@article{AnshuHarrowSoleimanifar2022,
  author = {Anshu, Anurag and Harrow, Aram W. and Soleimanifar, Mehdi},
  title = {Entanglement spread area law in gapped ground states},
  journal = {Nature Physics},
  volume = {18},
  pages = {1362--1366},
  year = {2022},
  doi = {10.1038/s41567-022-01740-7},
  eprint = {2004.15009},
  archivePrefix = {arXiv}
}

@article{AlickiFannes2004,
  author = {Alicki, Robert and Fannes, Mark},
  title = {Continuity of quantum conditional information},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {37}, number = {5}, pages = {L55--L57}, year = {2004},
  doi = {10.1088/0305-4470/37/5/L01},
  eprint = {quant-ph/0312081}, archivePrefix = {arXiv}
}

@article{LiebRobinson1972,
  author = {Lieb, Elliott H. and Robinson, Derek W.},
  title = {The finite group velocity of quantum spin systems},
  journal = {Communications in Mathematical Physics},
  volume = {28}, number = {3}, pages = {251--257}, year = {1972},
  doi = {10.1007/BF01645779}
}

@article{LewinNamRougerie2015,
  author = {Lewin, Mathieu and Nam, Phan Th{\`a}nh and Rougerie, Nicolas},
  title = {Remarks on the Quantum {de Finetti} Theorem for Bosonic Systems},
  journal = {Applied Mathematics Research eXpress},
  volume = {2015}, number = {1}, pages = {48--63}, year = {2015},
  doi = {10.1093/amrx/abu006},
  eprint = {1310.2200}, archivePrefix = {arXiv}
}

@article{KeylWerner2001,
  author = {Keyl, Michael and Werner, Reinhard F.},
  title = {Estimating the spectrum of a density operator},
  journal = {Physical Review A},
  volume = {64}, pages = {052311}, year = {2001},
  doi = {10.1103/PhysRevA.64.052311},
  eprint = {quant-ph/0102027}, archivePrefix = {arXiv}
}

@article{AradFirankoJain2026,
  author = {Arad, Itai and Firanko, Raz and Jain, Rahul},
  title = {Area Laws and Tensor Networks for Maximally Mixed Ground States},
  journal = {Communications in Mathematical Physics},
  volume = {407},
  number = {3},
  pages = {54},
  year = {2026},
  doi = {10.1007/s00220-026-05554-z},
  eprint = {2310.19028},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00220-026-05554-z}
}

@article{BombelliEtAl1986,
 author = {Bombelli, Luca and Koul, Rabinder K. and Lee, Joohan and Sorkin, Rafael D.},
 title = {Quantum source of entropy for black holes},
 journal = {Physical Review D}, volume = {34}, number = {2}, pages = {373--383},
 year = {1986}, doi = {10.1103/PhysRevD.34.373}
}
@article{Srednicki1993,
 author = {Srednicki, Mark}, title = {Entropy and area},
 journal = {Physical Review Letters}, volume = {71}, number = {5}, pages = {666--669},
 year = {1993}, doi = {10.1103/PhysRevLett.71.666},
 eprint = {hep-th/9303048}, archivePrefix = {arXiv}
}
@article{AradLandauVazirani2012,
 author = {Arad, Itai and Landau, Zeph and Vazirani, Umesh},
 title = {Improved one-dimensional area law for frustration-free systems},
 journal = {Physical Review B}, volume = {85}, pages = {195145}, year = {2012},
 doi = {10.1103/PhysRevB.85.195145}, eprint = {1111.2970}, archivePrefix = {arXiv}
}
@misc{AradKitaevLandauVazirani2013,
 author = {Arad, Itai and Kitaev, Alexei and Landau, Zeph and Vazirani, Umesh},
 title = {An area law and sub-exponential algorithm for {1D} systems},
 year = {2013}, eprint = {1301.1162}, archivePrefix = {arXiv}
}
@article{Masanes2009,
 author = {Masanes, Llu{\'i}s}, title = {Area law for the entropy of low-energy states},
 journal = {Physical Review A}, volume = {80}, pages = {052104}, year = {2009},
 doi = {10.1103/PhysRevA.80.052104}, eprint = {0907.4672}, archivePrefix = {arXiv}
}
@article{BrandaoCramer2015,
 author = {Brand{\~a}o, Fernando G. S. L. and Cramer, Marcus},
 title = {Entanglement area law from specific heat capacity},
 journal = {Physical Review B}, volume = {92}, pages = {115134}, year = {2015},
 doi = {10.1103/PhysRevB.92.115134}, eprint = {1409.5946}, archivePrefix = {arXiv}
}
@article{Cho2014,
 author = {Cho, Jaeyoon},
 title = {Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems},
 journal = {Physical Review Letters}, volume = {113}, pages = {197204}, year = {2014},
 doi = {10.1103/PhysRevLett.113.197204}, eprint = {1404.7616}, archivePrefix = {arXiv}
}
@article{VanAcoleyenMarienVerstraete2013,
 author = {Van Acoleyen, Karel and Mari{\"e}n, Micha{\"e}l and Verstraete, Frank},
 title = {Entanglement Rates and Area Laws},
 journal = {Physical Review Letters}, volume = {111}, pages = {170501}, year = {2013},
 doi = {10.1103/PhysRevLett.111.170501}, eprint = {1304.5931}, archivePrefix = {arXiv}
}

@article{KuboAndo1980,
  author = {Kubo, Fumio and Ando, Tsuyoshi},
  title = {Means of positive linear operators},
  journal = {Mathematische Annalen},
  volume = {246}, number = {3}, pages = {205--224}, year = {1980},
  doi = {10.1007/BF01371042}
}

@article{PuszWoronowicz1975,
  author = {Pusz, W. and Woronowicz, S. L.},
  title = {Functional calculus for sesquilinear forms and the purification map},
  journal = {Reports on Mathematical Physics},
  volume = {8}, number = {2}, pages = {159--170}, year = {1975},
  doi = {10.1016/0034-4877(75)90061-0}
}

@misc{OpenAI2026PolynomialPEPS,
  author = {{OpenAI}},
  title = {{Polynomial PEPS approximation of gapped square-grid ground states}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026/paper.pdf}{OAI:Polynomial-PEPS-approximation-of-gapped-square-grid-ground-states-September-24-2026}},
  year = {2026}
}

@article{NussbaumSzkola2009,
  author = {Nussbaum, Michael and Szko{\l}a, Arleta},
  title = {The {Chernoff} lower bound for symmetric quantum hypothesis testing},
  journal = {The Annals of Statistics},
  volume = {37},
  number = {2},
  pages = {1040--1057},
  year = {2009},
  doi = {10.1214/08-AOS593},
  eprint = {quant-ph/0607216},
  archivePrefix = {arXiv}
}

@article{Petz1986,
  author = {Petz, D{\'e}nes},
  title = {Sufficient subalgebras and the relative entropy of states of a von {Neumann} algebra},
  journal = {Communications in Mathematical Physics},
  volume = {105},
  number = {1},
  pages = {123--131},
  year = {1986},
  doi = {10.1007/BF01212345}
}

@article{ForresterIpsen2018,
  author = {Forrester, P. J. and Ipsen, J. R.},
  title = {Selberg integral theory and {Muttalib--Borodin} ensembles},
  journal = {Advances in Applied Mathematics},
  volume = {95},
  pages = {152--176},
  year = {2018},
  doi = {10.1016/j.aam.2017.11.004},
  eprint = {1612.06517},
  archivePrefix = {arXiv}
}

@article{RaggioWerner1989,
  author = {Raggio, G. A. and Werner, R. F.},
  title = {Quantum statistical mechanics of general mean field systems},
  journal = {Helvetica Physica Acta},
  volume = {62},
  number = {8},
  pages = {980--1003},
  year = {1989},
  doi = {10.5169/seals-116175}
}

@incollection{Chiribella2011,
  author = {Chiribella, Giulio},
  title = {On Quantum Estimation, Quantum Cloning and Finite Quantum {de Finetti} Theorems},
  booktitle = {Theory of Quantum Computation, Communication, and Cryptography},
  editor = {van Dam, Wim and Kendon, Vivien M. and Severini, Simone},
  series = {Lecture Notes in Computer Science},
  volume = {6519},
  pages = {9--25},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  year = {2011},
  doi = {10.1007/978-3-642-18073-6_2},
  eprint = {1010.1875},
  archivePrefix = {arXiv}
}

@article{VershikOkounkov2005,
  author = {Vershik, A. M. and Okounkov, A. Yu.},
  title = {A new approach to the representation theory of the symmetric groups. {II}},
  journal = {Journal of Mathematical Sciences},
  volume = {131},
  number = {2},
  pages = {5471--5494},
  year = {2005},
  doi = {10.1007/s10958-005-0421-7},
  eprint = {math/0503040},
  archivePrefix = {arXiv}
}

@article{BhatiaParthasarathy2000,
  author = {Bhatia, Rajendra and Parthasarathy, K. R.},
  title = {Positive definite functions and operator inequalities},
  journal = {Bulletin of the London Mathematical Society},
  volume = {32}, number = {2}, pages = {214--228}, year = {2000},
  doi = {10.1112/S0024609399006797}
}

@article{AnshuAradVidick2016,
  author = {Anshu, Anurag and Arad, Itai and Vidick, Thomas},
  title = {Simple proof of the detectability lemma and spectral gap amplification},
  journal = {Physical Review B},
  volume = {93}, pages = {205142}, year = {2016},
  doi = {10.1103/PhysRevB.93.205142},
  eprint = {1602.01210}, archivePrefix = {arXiv}
}

@article{BarthelKliesch2012,
  author = {Barthel, Thomas and Kliesch, Martin},
  title = {Quasilocality and efficient simulation of {Markovian} quantum dynamics},
  journal = {Physical Review Letters},
  volume = {108}, pages = {230504}, year = {2012},
  doi = {10.1103/PhysRevLett.108.230504},
  eprint = {1111.4210}, archivePrefix = {arXiv}
}

@misc{Tao247ANotes1,
  author = {Tao, Terence},
  title = {Lecture Notes 1 for 247A},
  howpublished = {UCLA course notes},
  note = {Lemma 5.10, pp.~13--14. \url{https://www.math.ucla.edu/~tao/247a.1.06f/notes1.pdf}},
  url = {https://www.math.ucla.edu/~tao/247a.1.06f/notes1.pdf}
}
