@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}
}

@misc{CarlenVershynina2019,
  author = {Carlen, Eric A. and Vershynina, Anna},
  title = {Recovery map stability for the Data Processing Inequality},
  year = {2019},
  eprint = {1710.02409},
  archivePrefix = {arXiv},
  note = {Version 3},
  url = {https://arxiv.org/pdf/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}
}



@misc{VerstraeteCirac2004PEPS,
  author = {Verstraete, F. and Cirac, J. I.},
  title = {Renormalization algorithms for {Quantum-Many Body Systems} in two and higher dimensions},
  year = {2004},
  eprint = {cond-mat/0407066},
  archivePrefix = {arXiv},
  primaryClass = {cond-mat.str-el},
  url = {https://arxiv.org/abs/cond-mat/0407066},
  note = {\href{https://arxiv.org/abs/cond-mat/0407066}{arXiv:cond-mat/0407066}}
}

@article{VerstraeteCirac2006MPS,
  author = {Verstraete, F. and Cirac, J. I.},
  title = {Matrix product states represent ground states faithfully},
  journal = {Physical Review B},
  volume = {73},
  pages = {094423},
  year = {2006},
  doi = {10.1103/PhysRevB.73.094423},
  eprint = {cond-mat/0505140},
  archivePrefix = {arXiv},
  primaryClass = {cond-mat.str-el},
  url = {https://arxiv.org/abs/cond-mat/0505140}
}

@article{SchuchWolfVerstraeteCirac2008,
  author = {Schuch, Norbert and Wolf, Michael M. and Verstraete, Frank and Cirac, J. Ignacio},
  title = {Entropy Scaling and Simulability by {Matrix Product States}},
  journal = {Physical Review Letters},
  volume = {100},
  pages = {030504},
  year = {2008},
  doi = {10.1103/PhysRevLett.100.030504},
  eprint = {0705.0292},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph},
  url = {https://arxiv.org/abs/0705.0292}
}

@article{MolnarSchuchVerstraeteCirac2015,
  author = {Moln{\'a}r, Andr{\'a}s and Schuch, Norbert and Verstraete, Frank and Cirac, J. Ignacio},
  title = {Approximating {Gibbs} states of local {Hamiltonians} efficiently with projected entangled pair states},
  journal = {Physical Review B},
  volume = {91},
  pages = {045138},
  year = {2015},
  doi = {10.1103/PhysRevB.91.045138},
  eprint = {1406.2973},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph},
  url = {https://arxiv.org/abs/1406.2973}
}

@misc{RepoAreaLaw,
  author = {{OpenAI}},
  title = {{A two-dimensional area law from a global spectral gap}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026/paper.pdf}{OAI:A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026}},
  year = {2026}
}

@article{CiracGarreRubioPerezGarcia2019,
  author = {Cirac, J. Ignacio and Garre-Rubio, Jos{\'e} and P{\'e}rez-Garc{\'i}a, David},
  title = {Mathematical open problems in projected entangled pair states},
  journal = {Revista Matem{\'a}tica Complutense},
  volume = {32}, number = {3}, pages = {579--599}, year = {2019},
  doi = {10.1007/s13163-019-00318-x},
  eprint = {1903.09439}, archivePrefix = {arXiv}
}
@article{GeEisert2016,
  author = {Ge, Yimin and Eisert, Jens},
  title = {Area laws and efficient descriptions of quantum many-body states},
  journal = {New Journal of Physics}, volume = {18}, number = {8},
  pages = {083026}, year = {2016},
  doi = {10.1088/1367-2630/18/8/083026},
  eprint = {1411.2995}, archivePrefix = {arXiv}
}
@article{Huang2026Local,
  author = {Huang, Yichen},
  title = {Approximating local properties by tensor network states with constant bond dimension},
  journal = {IEEE Transactions on Information Theory},
  volume = {72}, number = {7}, pages = {4930--4935}, year = {2026},
  doi = {10.1109/TIT.2026.3694133},
  eprint = {1903.10048}, archivePrefix = {arXiv},
  note = {Preprint first posted in 2019; arXiv:1903.10048}
}
@article{Hastings2006Local,
  author = {Hastings, M. B.},
  title = {Solving gapped {Hamiltonians} locally},
  journal = {Physical Review B}, volume = {73}, pages = {085115}, year = {2006},
  doi = {10.1103/PhysRevB.73.085115},
  eprint = {cond-mat/0508554}, archivePrefix = {arXiv}
}
@article{SchuchWolfVerstraeteCirac2007Complexity,
  author = {Schuch, Norbert and Wolf, Michael M. and Verstraete, Frank and Cirac, J. Ignacio},
  title = {Computational complexity of projected entangled pair states},
  journal = {Physical Review Letters}, volume = {98}, pages = {140506}, year = {2007},
  doi = {10.1103/PhysRevLett.98.140506},
  eprint = {quant-ph/0611050}, archivePrefix = {arXiv}
}
@article{SchwarzBuerschaperEisert2017,
  author = {Schwarz, M. and Buerschaper, O. and Eisert, J.},
  title = {Approximating local observables on projected entangled pair states},
  journal = {Physical Review A}, volume = {95}, pages = {060102(R)}, year = {2017},
  doi = {10.1103/PhysRevA.95.060102},
  eprint = {1606.06301}, 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}, pages = {54}, year = {2026},
  doi = {10.1007/s00220-026-05554-z},
  eprint = {2310.19028}, archivePrefix = {arXiv}
}

@article{Uhlmann1976,
  author = {Uhlmann, Armin},
  title = {The ``transition probability'' in the state space of a {$*$}-algebra},
  journal = {Reports on Mathematical Physics},
  volume = {9}, number = {2}, pages = {273--279}, year = {1976},
  doi = {10.1016/0034-4877(76)90060-4}
}

@article{CarlenLieb2014,
  author = {Carlen, Eric A. and Lieb, Elliott H.},
  title = {Remainder terms for some quantum entropy inequalities},
  journal = {Journal of Mathematical Physics},
  volume = {55}, number = {4}, pages = {042201}, year = {2014},
  doi = {10.1063/1.4871575},
  eprint = {1402.3840}, archivePrefix = {arXiv}, primaryClass = {quant-ph}
}

@phdthesis{Renner2005Security,
  author = {Renner, Renato},
  title = {Security of Quantum Key Distribution},
  school = {ETH Z{\"u}rich},
  year = {2005},
  note = {Diss. ETH No. 16242},
  eprint = {quant-ph/0512258},
  archivePrefix = {arXiv}
}

@article{DupuisBertaWullschlegerRenner2014,
  author = {Dupuis, Fr{\'e}d{\'e}ric and Berta, Mario and
            Wullschleger, J{\"u}rg and Renner, Renato},
  title = {One-Shot Decoupling},
  journal = {Communications in Mathematical Physics},
  volume = {328},
  pages = {251--284},
  year = {2014},
  doi = {10.1007/s00220-014-1990-4},
  eprint = {1012.6044},
  archivePrefix = {arXiv}
}

@article{Isserlis1918,
  author = {Isserlis, L.},
  title = {On a Formula for the Product-Moment Coefficient of Any Order
           of a Normal Frequency Distribution in Any Number of Variables},
  journal = {Biometrika},
  volume = {12},
  number = {1--2},
  pages = {134--139},
  year = {1918},
  doi = {10.1093/biomet/12.1-2.134}
}

@article{FassinoPistoneRogantin2019,
  author = {Fassino, Claudia and Pistone, Giovanni and Rogantin, Maria Piera},
  title = {Computing the Moments of the Complex Gaussian:
           Full and Sparse Covariance Matrix},
  journal = {Mathematics},
  volume = {7},
  number = {3},
  pages = {263},
  year = {2019},
  doi = {10.3390/math7030263}
}

@article{BarthelKlieschEisert2010,
  author = {Barthel, Thomas and Kliesch, Martin and Eisert, Jens},
  title = {Real-space renormalization yields finite correlations},
  journal = {Physical Review Letters},
  volume = {105},
  pages = {010502},
  year = {2010},
  doi = {10.1103/PhysRevLett.105.010502},
  eprint = {1003.2319v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1003.2319v2},
  note = {Section and equation numbers refer to arXiv:1003.2319v2}
}