@book{Griffiths2002,
  author = {Griffiths, Robert B.},
  title = {Consistent Quantum Theory},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {2002},
  doi = {10.1017/CBO9780511606052}
}

@article{Isham1997,
  author = {Isham, C. J.},
  title = {Topos Theory and Consistent Histories: The Internal Logic of the Set of All Consistent Sets},
  journal = {International Journal of Theoretical Physics},
  volume = {36},
  pages = {785--814},
  year = {1997},
  doi = {10.1007/BF02435786},
  eprint = {gr-qc/9607069},
  archivePrefix = {arXiv}
}

@article{Kent1997,
  author = {Kent, Adrian},
  title = {Consistent Sets Yield Contrary Inferences in Quantum Theory},
  journal = {Physical Review Letters},
  volume = {78},
  number = {15},
  pages = {2874--2877},
  year = {1997},
  doi = {10.1103/PhysRevLett.78.2874},
  eprint = {gr-qc/9604012},
  archivePrefix = {arXiv}
}

@article{Wallden2014,
  author = {Wallden, Petros},
  title = {Contrary Inferences in Consistent Histories and a Set Selection Criterion},
  journal = {Foundations of Physics},
  volume = {44},
  pages = {1195--1215},
  year = {2014},
  doi = {10.1007/s10701-014-9837-6},
  eprint = {1402.3733},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{LeggettGarg1985,
  author = {Leggett, A. J. and Garg, Anupam},
  title = {Quantum Mechanics versus Macroscopic Realism: Is the Flux There when Nobody Looks?},
  journal = {Physical Review Letters},
  volume = {54},
  number = {9},
  pages = {857--860},
  year = {1985},
  doi = {10.1103/PhysRevLett.54.857}
}

@article{HalliwellMawby2019,
  author = {Halliwell, J. J. and Mawby, C.},
  title = {{Fine}'s Theorem for {Leggett--Garg} Tests with an Arbitrary Number of Measurement Times},
  journal = {Physical Review A},
  volume = {100},
  number = {4},
  pages = {042103},
  year = {2019},
  doi = {10.1103/PhysRevA.100.042103},
  eprint = {1906.04865},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{RobertsonEtAl2025,
  author = {Robertson, Sawyer Jack and Kohli, Dhruv and Mishne, Gal and Cloninger, Alexander},
  title = {On a Generalization of {Wasserstein} Distance and the {Beckmann} Problem to Connection Graphs},
  journal = {SIAM Journal on Scientific Computing},
  volume = {47},
  number = {5},
  pages = {A2774--A2800},
  year = {2025},
  doi = {10.1137/23M1624828},
  eprint = {2312.10295v3},
  archivePrefix = {arXiv}
}

@article{AbramskyBrandenburger2011,
  author = {Abramsky, Samson and Brandenburger, Adam},
  title = {The Sheaf-Theoretic Structure of Non-Locality and Contextuality},
  journal = {New Journal of Physics},
  volume = {13},
  number = {11},
  pages = {113036},
  year = {2011},
  doi = {10.1088/1367-2630/13/11/113036},
  eprint = {1102.0264},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{Halliwell2017,
  author = {Halliwell, J. J.},
  title = {Incompatible Multiple Consistent Sets of Histories and Measures of Quantumness},
  journal = {Physical Review A},
  volume = {96},
  number = {1},
  pages = {012123},
  year = {2017},
  doi = {10.1103/PhysRevA.96.012123},
  eprint = {1704.01783},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{DowkerHensonWallden2014,
  author = {Dowker, Fay and Henson, Joe and Wallden, Petros},
  title = {A Histories Perspective on Characterizing Quantum Non-Locality},
  journal = {New Journal of Physics},
  volume = {16},
  number = {3},
  pages = {033033},
  year = {2014},
  doi = {10.1088/1367-2630/16/3/033033},
  eprint = {1311.6287},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{CraigEtAl2007,
  author = {Craig, David and Dowker, Fay and Henson, Joe and Major, Seth and Rideout, David and Sorkin, Rafael D.},
  title = {A {Bell} Inequality Analog in Quantum Measure Theory},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {40},
  number = {3},
  pages = {501--523},
  year = {2007},
  doi = {10.1088/1751-8113/40/3/010},
  eprint = {quant-ph/0605008},
  archivePrefix = {arXiv}
}

@article{Gudder2012,
  author = {Gudder, Stan},
  title = {{Hilbert} Space Representations of Decoherence Functionals and Quantum Measures},
  journal = {Mathematica Slovaca},
  volume = {62},
  number = {6},
  pages = {1209--1230},
  year = {2012},
  doi = {10.2478/s12175-012-0074-1},
  eprint = {1011.1694},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{GoldsteinPage1995,
  author = {Goldstein, Sheldon and Page, Don N.},
  title = {Linearly Positive Histories: Probabilities for a Robust Family of Sequences of Quantum Events},
  journal = {Physical Review Letters},
  volume = {74},
  number = {19},
  pages = {3715--3719},
  year = {1995},
  doi = {10.1103/PhysRevLett.74.3715},
  eprint = {gr-qc/9403055},
  archivePrefix = {arXiv}
}

@article{HalliwellYearsley2013,
  author = {Halliwell, J. J. and Yearsley, J. M.},
  title = {Negative Probabilities, {Fine}'s Theorem, and Linear Positivity},
  journal = {Physical Review A},
  volume = {87},
  number = {2},
  pages = {022114},
  year = {2013},
  doi = {10.1103/PhysRevA.87.022114}
}

@incollection{DeBarrosEtAl2016,
  author = {{de Barros}, J. Acacio and Dzhafarov, Ehtibar N. and Kujala, Janne V. and Oas, Gary},
  title = {Measuring Observable Quantum Contextuality},
  booktitle = {Quantum Interaction},
  editor = {Atmanspacher, Harald and Filk, Thomas and Pothos, Emmanuel},
  series = {Lecture Notes in Computer Science},
  volume = {9535},
  pages = {36--47},
  publisher = {Springer},
  address = {Cham},
  year = {2016},
  doi = {10.1007/978-3-319-28675-4_4},
  eprint = {1406.3088},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{AbramskyBarbosaMansfield2017,
  author = {Abramsky, Samson and Barbosa, Rui Soares and Mansfield, Shane},
  title = {Contextual Fraction as a Measure of Contextuality},
  journal = {Physical Review Letters},
  volume = {119},
  number = {5},
  pages = {050504},
  year = {2017},
  doi = {10.1103/PhysRevLett.119.050504}
}

@article{Vorobev1962,
  author = {Vorob'ev, N. N.},
  title = {Consistent Families of Measures and Their Extensions},
  journal = {Theory of Probability and Its Applications},
  volume = {7},
  number = {2},
  pages = {147--163},
  year = {1962},
  doi = {10.1137/1107014}
}

@article{Strassen1965,
  author = {Strassen, Volker},
  title = {The Existence of Probability Measures with Given Marginals},
  journal = {The Annals of Mathematical Statistics},
  volume = {36},
  number = {2},
  pages = {423--439},
  year = {1965},
  doi = {10.1214/aoms/1177700153}
}

@book{HeindorfShapiro1994,
  author = {Heindorf, Lutz and Shapiro, Leonid B.},
  title = {Nearly Projective {Boolean} Algebras},
  series = {Lecture Notes in Mathematics},
  volume = {1596},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  year = {1994},
  note = {With an appendix by Saka{\'e} Fuchino},
  doi = {10.1007/BFb0094103},
  isbn = {978-3-540-58787-3}
}

@misc{Milovich2016,
  author = {Milovich, David},
  title = {Amalgamating Many Overlapping {Boolean} Algebras},
  year = {2016},
  eprint = {1607.07944v1},
  archivePrefix = {arXiv},
  primaryClass = {math.LO},
  url = {https://arxiv.org/abs/1607.07944v1},
  note = {arXiv:1607.07944v1}
}

@incollection{AtseriasKolaitis2023,
  author = {Atserias, Albert and Kolaitis, Phokion G.},
  title = {Consistency, Acyclicity, and Positive Semirings},
  booktitle = {Samson Abramsky on Logic and Structure in Computer Science and Beyond},
  editor = {Palmigiano, Alessandra and Sadrzadeh, Mehrnoosh},
  series = {Outstanding Contributions to Logic},
  volume = {25},
  pages = {623--668},
  publisher = {Springer},
  address = {Cham},
  year = {2023},
  doi = {10.1007/978-3-031-24117-8_17},
  eprint = {2009.09488},
  archivePrefix = {arXiv},
  primaryClass = {cs.DB}
}

@article{ZhouEtAl2020,
  author = {Zhou, Li and Ying, Shenggang and Yu, Nengkun and Ying, Mingsheng},
  title = {{Strassen}'s Theorem for Quantum Couplings},
  journal = {Theoretical Computer Science},
  volume = {802},
  pages = {67--76},
  year = {2020},
  doi = {10.1016/j.tcs.2019.08.026}
}

@article{BhatiaJainLim2019,
  author = {Bhatia, Rajendra and Jain, Tanvi and Lim, Yongdo},
  title = {On the {Bures--Wasserstein} Distance between Positive Definite Matrices},
  journal = {Expositiones Mathematicae},
  volume = {37},
  number = {2},
  pages = {165--191},
  year = {2019},
  doi = {10.1016/j.exmath.2018.01.002},
  eprint = {1712.01504},
  archivePrefix = {arXiv},
  primaryClass = {math.FA}
}

@article{Schonemann1966,
  author = {Sch{\"o}nemann, Peter H.},
  title = {A Generalized Solution of the Orthogonal {Procrustes} Problem},
  journal = {Psychometrika},
  volume = {31},
  number = {1},
  pages = {1--10},
  year = {1966},
  doi = {10.1007/BF02289451}
}

@book{LyonsPeres2016,
  author = {Lyons, Russell and Peres, Yuval},
  title = {Probability on Trees and Networks},
  series = {Cambridge Series in Statistical and Probabilistic Mathematics},
  volume = {42},
  publisher = {Cambridge University Press},
  year = {2016},
  doi = {10.1017/9781316672815},
  url = {https://rdlyons.pages.iu.edu/prbtree/}
}

@article{DowkerHalliwell1992,
  author = {Dowker, H. F. and Halliwell, J. J.},
  title = {Quantum Mechanics of History: The Decoherence Functional in Quantum Mechanics},
  journal = {Physical Review D},
  volume = {46},
  number = {4},
  pages = {1580--1609},
  year = {1992},
  doi = {10.1103/PhysRevD.46.1580}
}

@article{DowkerWilkes2022,
  author = {Dowker, Fay and Wilkes, Henry},
  title = {An Argument for Strong Positivity of the Decoherence Functional in the Path Integral Approach to the Foundations of Quantum Theory},
  journal = {AVS Quantum Science},
  volume = {4},
  number = {1},
  pages = {012601},
  year = {2022},
  doi = {10.1116/5.0073587},
  eprint = {2011.06120},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{NapoliEtAl2016,
  author = {Napoli, Carmine and Bromley, Thomas R. and Cianciaruso, Marco and Piani, Marco and Johnston, Nathaniel and Adesso, Gerardo},
  title = {Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence},
  journal = {Physical Review Letters},
  volume = {116},
  number = {15},
  pages = {150502},
  year = {2016},
  doi = {10.1103/PhysRevLett.116.150502},
  eprint = {1601.03781},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@article{PianiEtAl2016,
  author = {Piani, Marco and Cianciaruso, Marco and Bromley, Thomas R. and Napoli, Carmine and Johnston, Nathaniel and Adesso, Gerardo},
  title = {Robustness of Asymmetry and Coherence of Quantum States},
  journal = {Physical Review A},
  volume = {93},
  number = {4},
  pages = {042107},
  year = {2016},
  doi = {10.1103/PhysRevA.93.042107},
  eprint = {1601.03782},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}

@incollection{GellMannHartle1994,
  author = {Gell-Mann, Murray and Hartle, James B.},
  title = {Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology},
  booktitle = {Physical Origins of Time Asymmetry},
  editor = {Halliwell, J. J. and P{\'e}rez-Mercader, J. and Zurek, W. H.},
  pages = {311--345},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {1994},
  eprint = {gr-qc/9304023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/gr-qc/9304023}
}

@article{CheflesJozsaWinter2004,
  author = {Chefles, Anthony and Jozsa, Richard and Winter, Andreas},
  title = {On the Existence of Physical Transformations between Sets of Quantum States},
  journal = {International Journal of Quantum Information},
  volume = {2},
  number = {1},
  pages = {11--21},
  year = {2004},
  doi = {10.1142/S0219749904000031},
  eprint = {quant-ph/0307227},
  archivePrefix = {arXiv}
}

@article{ChildsWiebe2012,
  author = {Childs, Andrew M. and Wiebe, Nathan},
  title = {{Hamiltonian} Simulation Using Linear Combinations of Unitary Operations},
  journal = {Quantum Information and Computation},
  volume = {12},
  number = {11--12},
  pages = {901--924},
  year = {2012},
  doi = {10.26421/QIC12.11-12-1},
  eprint = {1202.5822},
  archivePrefix = {arXiv},
  primaryClass = {quant-ph}
}