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We introduce Inflation, a Python library for assessing whether an observed probability distribution is compatible with a causal explanation.
“Limits on correlations in networks for quantum and no-signaling resources”
Marc-Olivier Renou, Yuyi Wang, Sadra Boreiri, Salman Beigi, Nicolas Gisin, and Nicolas Brunner · 1901
Earlier work this paper cites.
“Bounding the sets of classical and quantum correlations in networks”
Alejandro Pozas-Kerstjens, Rafael Rabelo, Łukasz Rudnicki, Rafael Chaves, Daniel Cavalcanti, Miguel Navascués, and Antonio Acín · 1904
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Iris Agresti, Davide Poderini, Leonardo Guerini, Michele Mancusi, Gonzalo Carvacho, Leandro Aolita, Daniel Cavalcanti, Rafael Chaves, and Fabio Sciarrino · 1905
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“Constraints on nonlocality in networks from no-signaling and independence”
Nicolas Gisin, Jean-Daniel Bancal, Yu Cai, Patrick Remy, Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Sandu Popescu, and Nicolas Brunner · 1906
Earlier work this paper cites.
“Quantum inflation: A general approach to quantum causal compatibility”
Elie Wolfe, Alejandro Pozas-Kerstjens, Matan Grinberg, Denis Rosset, Antonio Acín, and Miguel Navascués · 1909
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“RepLAB: A computational/numerical approach to representation theory”
Denis Rosset, Felipe Montealegre-Mora, and Jean-Daniel Bancal · 1911
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“On the Einstein-Podolsky-Rosen paradox”
John S. Bell · 1964
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“Quantum mysteries revisited”
N. David Mermin · 1990
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“Quantifier elimination for statistical problems”
Dan Geiger and Christopher Meek · 1995
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“SDPT3 — a MATLAB software package for semidefinite programming”
Kim-Chuan Toh, Michael J. Todd, and Reha H. Tütüncü · 1999
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Daniel Brosch and Etienne de Klerk · 2001
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“On the testable implications of causal models with hidden variables”
Jin Tian and Judea Pearl · 2002
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“Semidefinite tests for quantum network topologies”
Johan Åberg, Ranieri Nery, Cristhiano Duarte, and Rafael Chaves · 2002
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“YALMIP: A toolbox for modeling and optimization in MATLAB”
Johann Löfberg · 2004
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“Algebraic geometry of Bayesian networks”
Luis David Garcia, Michael Stillman, and Bernd Sturmfels · 2005
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“Bounding the set of quantum correlations”
Miguel Navascués, Stefano Pironio, and Antonio Acín · 2007
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“Quantifying causal influences in the presence of a quantum common cause”
Mariami Gachechiladze, Nikolai Miklin, and Rafael Chaves · 2007
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“A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations”
Miguel Navascués, Stefano Pironio, and Antonio Acín · 2008
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“Causality: Models, Reasoning, and Inference”
Judea Pearl · 2009
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“Characterizing the nonlocal correlations created via entanglement swapping”
Cyril Branciard, Nicolas Gisin, and Stefano Pironio · 2010
Cited alongside, same era.
“Convergent relaxations of polynomial optimization problems with non-commuting variables”
Stefano Pironio, Miguel Navascués, and Antonio Acín · 2010
Cited alongside, same era.
“A sequence of relaxations constraining hidden variable models”
Greg ver Steeg and Aram Galstyan · 2011
Cited alongside, same era.
“Bilocal versus nonbilocal correlations in entanglement-swapping experiments”
Cyril Branciard, Denis Rosset, Nicolas Gisin, and Stefano Pironio · 2012
Cited alongside, same era.
“Quantum violations in the Instrumental scenario and their relations to the Bell scenario”
Thomas van Himbeeck, Jonatan Bohr Brask, Stefano Pironio, Ravishankar Ramanathan, Ana Belén Sainz, and Elie Wolfe · 2019
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“The inflation technique for causal inference with latent variables”
Elie Wolfe, Robert W. Spekkens, and Tobias Fritz · 2019
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“MOSEK Fusion API for Python”
MOSEK ApS · 2019
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“Quantum information outside quantum information”
Alejandro Pozas-Kerstjens · 2019
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“Semidefinite tests for latent causal structures”
Aditya Kela, Kai Von Prillwitz, Johan Åberg, Rafael Chaves, and David Gross · 2020
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Tobias Fritz · 2012
Cited alongside, same era.
“Hardy’s non-locality paradox and possibilistic conditions for non-locality”
Shane Mansfield and Tobias Fritz · 2012
Cited alongside, same era.
“Device-independent entanglement quantification and related applications”
Tobias Moroder, Jean-Daniel Bancal, Yeong-Cherng Liang, Martin Hofmann, and Otfried Gühne · 2013
Cited alongside, same era.
“Algebraic statistics in model selection”
Luis David Garcia · 2014
Cited alongside, same era.
Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner · 2014
Cited alongside, same era.
Christopher J. Wood and Robert W. Spekkens · 2015
Cited alongside, same era.
“Unifying framework for relaxations of the causal assumptions in Bell’s theorem”
Rafael Chaves, Richard Kueng, Jonatan B. Brask, and David Gross · 2015
Cited alongside, same era.
“Numba: A LLVM-based Python JIT compiler”
Siu Kwan Lam, Antoine Pitrou, and Stanley Seibert · 2015
Cited alongside, same era.
“The inflation technique completely solves the causal compatibility problem”
Miguel Navascués and Elie Wolfe · 2020
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“Array programming with NumPy”
Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, et al · 2020
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“SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python”
Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, et al · 2020
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“A convergent inflation hierarchy for quantum causal structures” (2021)
Laurens T. Ligthart, Mariami Gachechiladze, and David Gross · 2021
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“SCS: Splitting Conic Solver”
Brendan O’Donoghue, Eric Chu, Neal Parikh, and Stephen Boyd · 2021
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“Bell nonlocality in networks”
Armin Tavakoli, Alejandro Pozas-Kerstjens, Ming-Xing Luo, and Marc-Olivier Renou · 2022
Closest in time.
Alejandro Pozas-Kerstjens, Nicolas Gisin, and Armin Tavakoli · 2022
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“Source code for inflation
Emanuel-Cristian Boghiu, Elie Wolfe, and Alejandro Pozas-Kerstjens · 2022
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Laurens T. Ligthart and David Gross · 2022
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“Single-photon nonlocality in quantum networks”
Paolo Abiuso, Tamás Kriváchy, Emanuel-Cristian Boghiu, Marc-Olivier Renou, Alejandro Pozas-Kerstjens, and Antonio Acín · 2022
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“Experimental test of quantum causal influences”
Iris Agresti, Davide Poderini, Beatrice Polacchi, Nikolai Miklin, Mariami Gachechiladze, Alessia Suprano, Emanuele Polino, Giorgio Milani, Gonzalo Carvacho, Rafael Chaves, and Fabio Sciarrino · 2022
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“Gurobi Optimizer Reference Manual”
Gurobi Optimization, LLC · 2022
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“PICOS: A Python interface to conic optimization solvers”
Guillaume Sagnol and Maximilian Stahlberg · 2022
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“Proofs of network quantum nonlocality in continuous families of distributions”
Alejandro Pozas-Kerstjens, Nicolas Gisin, and Marc-Olivier Renou · 2023
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