[19] T. Vértesi and E. Bene, Lower bound on the com-
munication cost of simulating bipartite quantum
correlations, Phys. Rev. A 80, 062316 (2009).
[20] M. J. W. Hall, Relaxed Bell inequalities and
Kochen-Specker theorems, Phys. Rev. A 84,
022102 (2011).
[21] K. Maxwell and E. Chitambar, Bell inequalities
with communication assistance, Phys. Rev. A 89,
042108 (2014).
[22] R. Chaves, R. Kueng, J. B. Brask, and
D. Gross, Unifying Framework for Relaxations
of the Causal Assumptions in Bell’s Theorem,
Phys. Rev. Lett. 114, 140403 (2015).
[23] J. B. Brask and R. Chaves, Bell scenarios with
communication, J. Phys. A 50, 094001 (2017).
[24] M. Ringbauer, C. Giarmatzi, R. Chaves,
F. Costa, A. G. White, and A. Fedrizzi, Ex-
perimental test of nonlocal causality, Sci. Adv. 2,
e1600162 (2016).
[25] R. Chaves, D. Cavalcanti, and L. Aolita, Causal
hierarchy of multipartite Bell nonlocality, Quan-
tum 1, 23 (2017).
[26] C. J. Wood and R. W. Spekkens, The lesson
of causal discovery algorithms for quantum cor-
relations: Causal explanations of Bell-inequality
violations require fine-tuning, New J. Phys. 17,
033002 (2015).
[27] A. J. Leggett and A. Garg, Quantum mechan-
ics versus macroscopic realism: Is the flux there
when nobody looks? Phys. Rev. Lett. 54, 857
(1985).
[28] J. Pearl, Causality (Cambridge University Press,
2009).
[29] J. S. Bell, The theory of local beables, Epistem.
Lett. 9, 11 (1976).
[30] C. H. Bennett, G. Brassard, C. Crépeau,
R. Jozsa, A. Peres, and W. K. Wootters,
Teleporting an unknown quantum state via dual
classical and Einstein-Podolsky-Rosen channels,
Phys. Rev. Lett. 70, 1895 (1993).
[31] C. H. Bennett and S. J. Wiesner, Communication
via one- and two-particle operators on Einstein-
Podolsky-Rosen states, Phys. Rev. Lett. 69, 2881
(1992).
[32] H. J. Briegel, D. E. Browne, W. Dür,
R. Raussendorf, and M. Van den Nest,
Measurement-based quantum computation, Nat.
Phys. , 19 (2009).
[33] S. Popescu, Bell’s Inequalities and Density Ma-
trices: Revealing “Hidden” Nonlocality, Phys.
Rev. Lett. 74, 2619 (1995).
[34] R. Gallego, L. E. Würflinger, R. Chaves, A. Acín,
and M. Navascués, Nonlocality in sequential cor-
relation scenarios, New J. Phys. 16, 033037
(2014).
[35] N. Langford, T. Weinhold, R. Prevedel,
K. Resch, A. Gilchrist, J. O’Brien, G. Pryde, and
A. White, Demonstration of a Simple Entangling
Optical Gate and Its Use in Bell-State Analysis,
Phys. Rev. Lett. 95, 210504 (2005).
[36] S. Hill and W. K. Wootters, Entanglement of a
Pair of Quantum Bits, Phys. Rev. Lett. 78, 5022
(1997).
[37] N. Harrigan and R. W. Spekkens, Einstein, In-
completeness, and the Epistemic View of Quan-
tum States, Found. Phys. 40, 125 (2010).
[38] M. J. W. Hall, Local Deterministic Model of Sin-
glet State Correlations Based on Relaxing Mea-
surement Independence, Phys. Rev. Lett. 105,
250404 (2010).
[39] R. Chaves, Polynomial Bell Inequalities, Phys.
Rev. Lett. 116, 010402 (2016).
[40] C. M. Lee and R. W. Spekkens, Causal Infer-
ence via Algebraic Geometry: Feasibility Tests
for Functional Causal Structures with Two Bi-
nary Observed Variables, J. Causal Inference 5,
6 (2017).
[41] C. Emary, N. Lambert, and F. Nori,
Leggett–Garg inequalities, Rep. Prog. Phys. 77,
016001 (2014).
[42] L. Clemente and J. Kofler, Necessary and suf-
ficient conditions for macroscopic realism from
quantum mechanics, Phys. Rev. A 91, 062103
(2015).
[43] M. Ringbauer, C. J. Wood, K. Modi,
A. Gilchrist, A. G. White, and A. Fedrizzi,
Characterizing Quantum Dynamics with Initial
System-Environment Correlations, Phys. Rev.
Lett. 114, 090402 (2015).
[44] H. Buhrman, R. Cleve, S. Massar, and R. De
Wolf, Nonlocality and communication complex-
ity, Rev. Mod. Phys. 82, 665 (2010).
[45] M. Pawłowski, T. Paterek, D. Kaszlikowski,
V. Scarani, A. Winter, and M. Zukowski, Infor-
mation causality as a physical principle. Nature
461, 1101 (2009).
[46] T. Christof and A. Löbel, PORTA – POlyhedron
Representation Transformation Algorithm,
(2009).
[47] J. Clauser, M. Horne, A. Shimony, and R. Holt,
Proposed Experiment to Test Local Hidden-
Variable Theories, Phys. Rev. Lett. 23, 880
(1969).
[48] R. Horodecki, P. Horodecki, and M. Horodecki,
Violating Bell inequality by mixed spin-12 states:
necessary and sufficient condition, Phys. Lett. A
200, 340 (1995).
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