Postquantum common-cause channels: the resource theory of local operations and shared entanglement

David Schmid; Haoxing Du; Maryam Mudassar; Ghi Coulter-de Wit; Denis Rosset; Matty J. Hoban

doi:10.22331/q-2021-03-23-419

Postquantum common-cause channels: the resource theory of local operations and shared entanglement

David Schmid^1,2, Haoxing Du¹, Maryam Mudassar¹, Ghi Coulter-de Wit¹, Denis Rosset¹, and Matty J. Hoban³

¹Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
²Institute for Quantum Computing and Dept. of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
³Department of Computing, Goldsmiths, University of London, New Cross, London SE14 6NW, United Kingdom

Published:	2021-03-23, volume 5, page 419
Eprint:	arXiv:2004.06133v4
Doi:	https://doi.org/10.22331/q-2021-03-23-419
Citation:	Quantum 5, 419 (2021).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We define the type-independent resource theory of local operations and shared entanglement (LOSE). This allows us to formally quantify postquantumness in common-cause scenarios such as the Bell scenario. Any nonsignaling bipartite quantum channel which cannot be generated by LOSE operations requires a $\textit{postquantum common cause}$ to generate, and constitutes a valuable resource. Our framework allows LOSE operations that arbitrarily transform between different types of resources, which in turn allows us to undertake a systematic study of the different manifestations of postquantum common causes. Only three of these have been previously recognized, namely postquantum correlations, postquantum steering, and non-localizable channels, all of which are subsumed as special cases of resources in our framework. Finally, we prove several fundamental results regarding how the type of a resource determines what conversions into other resources are possible, and also places constraints on the resource's ability to provide an advantage in distributed tasks such as nonlocal games, semiquantum games, steering games, etc.

Featured image: A sampling of different types of nonsignaling resources that fit into our unified framework: quantum states, steering assemblages, quantum teleportages, nonlocal boxes, measurement-device-independent boxes, channel steering assemblages, Bob-with-input assemblages, and ensemble-preparations. We prove that all and only resource types with nontrivial inputs and outputs for both parties admit of postquantumness.

► BibTeX data

@article{Schmid2021postquantumcommon,
  doi = {10.22331/q-2021-03-23-419},
  url = {https://doi.org/10.22331/q-2021-03-23-419},
  title = {Postquantum common-cause channels: the resource theory of local operations and shared entanglement},
  author = {Schmid, David and Du, Haoxing and Mudassar, Maryam and Coulter-de Wit, Ghi and Rosset, Denis and Hoban, Matty J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {419},
  month = mar,
  year = {2021}
}

► References

[1] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014a).
https://doi.org/10.1103/RevModPhys.86.419

[2] C. J. Wood and R. W. Spekkens, New J. Phys. 17, 033002 (2015).
https://doi.org/10.1088/1367-2630/17/3/033002

[3] J.-M. A. Allen, J. Barrett, D. C. Horsman, C. M. Lee, and R. W. Spekkens, Phys. Rev. X 7, 031021 (2017).
https://doi.org/10.1103/PhysRevX.7.031021

[4] J. Barrett, R. Lorenz, and O. Oreshkov, (2019), arXiv:1906.10726.
arXiv:1906.10726

[5] F. Costa and S. Shrapnel, New J. Phys 18, 063032 (2016).
https://doi.org/10.1088/1367-2630/18/6/063032

[6] B. S. Cirel'son, Letters in Mathematical Physics 4, 93 (1980).
https://doi.org/10.1007/BF00417500

[7] S. Popescu and D. Rohrlich, Foundations of Physics 24, 379 (1994).
https://doi.org/10.1007/BF02058098

[8] J. Barrett, Phys. Rev. A 75, 032304 (2007).
https://doi.org/10.1103/PhysRevA.75.032304

[9] L. Hardy, arXiv:quant-ph/0101012 (2001).
arXiv:quant-ph/0101012

[10] E. Wolfe, D. Schmid, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, Quantum 4, 280 (2020).
https://doi.org/10.22331/q-2020-06-08-280

[11] D. Beckman, D. Gottesman, M. A. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
https://doi.org/10.1103/PhysRevA.64.052309

[12] M. Piani, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 74, 012305 (2006).
https://doi.org/10.1103/PhysRevA.74.012305

[13] G. M. D'Ariano, S. Facchini, and P. Perinotti, Phys. Rev. Lett. 106, 010501 (2011).
https://doi.org/10.1103/PhysRevLett.106.010501

[14] M. J. Hoban and A. B. Sainz, New Journal of Physics 20, 053048 (2018).
https://doi.org/10.1088/1367-2630/aabea8

[15] A. Belén Sainz, M. J. Hoban, P. Skrzypczyk, and L. Aolita, (2019), arXiv:1907.03705.
https://doi.org/10.1103/PhysRevLett.125.050404
arXiv:1907.03705

[16] G. Gutoski, (2008), arXiv:0805.2209.
arXiv:0805.2209

[17] A. B. Sainz, N. Brunner, D. Cavalcanti, P. Skrzypczyk, and T. Vértesi, Phys. Rev. Lett. 115, 190403 (2015).
https://doi.org/10.1103/PhysRevLett.115.190403

[18] A. B. Sainz, L. Aolita, M. Piani, M. J. Hoban, and P. Skrzypczyk, New Journal of Physics 20, 083040 (2018).
https://doi.org/10.1088/1367-2630/aad8df

[19] B. Coecke, T. Fritz, and R. W. Spekkens, Information and Computation 250, 59 (2016), Quantum Physics and Logic.
https://doi.org/10.1016/j.ic.2016.02.008

[20] G. Chiribella and R. W. Spekkens, Quantum theory: informational foundations and foils (Springer, 2016).

[21] L. Hardy, ``Probability theories with dynamic causal structure: A new framework for quantum gravity,'' (2005), arXiv:gr-qc/0509120 [gr-qc].
arXiv:gr-qc/0509120

[22] M. Navascués and H. Wunderlich, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, 881 (2010), publisher: Royal Society.
https://doi.org/10.1098/rspa.2009.0453

[23] M. Pawłowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Żukowski, Nature 461, 1101 (2009), number: 7267 Publisher: Nature Publishing Group.
https://doi.org/10.1038/nature08400

[24] M. Pawłowski and V. Scarani, in Quantum Theory: Informational Foundations and Foils, Fundamental Theories of Physics, edited by G. Chiribella and R. W. Spekkens (Springer Netherlands, Dordrecht, 2016) pp. 423–438.
https://doi.org/10.1007/978-94-017-7303-4_12

[25] G. Brassard, H. Buhrman, N. Linden, A. A. Méthot, A. Tapp, and F. Unger, Physical Review Letters 96, 250401 (2006), publisher: American Physical Society.
https://doi.org/10.1103/PhysRevLett.96.250401

[26] N. Linden, S. Popescu, A. J. Short, and A. Winter, Physical Review Letters 99, 180502 (2007), publisher: American Physical Society.
https://doi.org/10.1103/PhysRevLett.99.180502

[27] A. Broadbent, Physical Review A 94, 022318 (2016), publisher: American Physical Society.
https://doi.org/10.1103/PhysRevA.94.022318

[28] T. Fritz, A. B. Sainz, R. Augusiak, J. B. Brask, R. Chaves, A. Leverrier, and A. Acín, Nature Communications 4, 1 (2013), number: 1 Publisher: Nature Publishing Group.
https://doi.org/10.1038/ncomms3263

[29] A. Cabello, arXiv:1212.1756 (2012), arXiv: 1212.1756.
arXiv:1212.1756

[30] T. Gonda, R. Kunjwal, D. Schmid, E. Wolfe, and A. B. Sainz, Quantum 2 (2018), 10.22331/q-2018-08-27-87.
https://doi.org/10.22331/q-2018-08-27-87

[31] M. Navascués, Y. Guryanova, M. J. Hoban, and A. Acín, Nature Communications 6, 6288 (2015).
https://doi.org/10.1038/ncomms7288

[32] J. Henson and A. B. Sainz, Physical Review A 91, 042114 (2015).
https://doi.org/10.1103/PhysRevA.91.042114

[33] M. Navascués, S. Pironio, and A. Acín, Phys. Rev. Lett. 98, 010401 (2007).
https://doi.org/10.1103/PhysRevLett.98.010401

[34] T. H. Yang, T. Vértesi, J.-D. Bancal, V. Scarani, and M. Navascués, Phys. Rev. Lett. 113, 040401 (2014).
https://doi.org/10.1103/PhysRevLett.113.040401

[35] I. Šupić, M. J. Hoban, L. D. Colomer, and A. Acín, arXiv:quant-ph/1911.09395 (2019).
https://doi.org/10.1088/1367-2630/ab90d1
arXiv:1911.09395

[36] R. Colbeck, arXiv:quant-ph/0911.3814 (2009).
arXiv:0911.3814

[37] R. Colbeck and A. Kent, Journal of Physics A: Mathematical and Theoretical 44, 095305 (2011).
https://doi.org/10.1088/1751-8113/44/9/095305

[38] S. Pironio, A. Acín, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, Nature 464, 1021 (2010).
https://doi.org/10.1038/nature09008

[39] I. Šupić, P. Skrzypczyk, and D. Cavalcanti, Physical Review A 95, 042340 (2017).
https://doi.org/10.1103/PhysRevA.95.042340

[40] A. C. Doherty, Y. Liang, B. Toner, and S. Wehner, in 2008 23rd Annual IEEE Conference on Computational Complexity (2008) pp. 199–210.

[41] M. D. Mazurek, M. F. Pusey, K. J. Resch, and R. W. Spekkens, arXiv:1710.05948 (2019), arXiv: 1710.05948.
arXiv:1710.05948

[42] Y.-C. Liang and Y. Zhang, Entropy 21, 185 (2019), number: 2 Publisher: Multidisciplinary Digital Publishing Institute.
https://doi.org/10.3390/e21020185

[43] D. Schmid, D. Rosset, and F. Buscemi, Quantum 4, 262 (2020a).
https://doi.org/10.22331/q-2020-04-30-262

[44] D. Schmid, J. H. Selby, and R. W. Spekkens, ``Unscrambling the omelette of causation and inference: The framework of causal-inferential theories,'' (2020b), arXiv:2009.03297 [quant-ph].
arXiv:2009.03297

[45] D. Rosset, D. Schmid, and F. Buscemi, Phys. Rev. Lett. 125, 210402 (2020).
https://doi.org/10.1103/PhysRevLett.125.210402

[46] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2010).
https://doi.org/10.1017/CBO9780511976667

[47] D. Schmid, K. Ried, and R. W. Spekkens, Phys. Rev. A 100, 022112 (2019a).
https://doi.org/10.1103/PhysRevA.100.022112

[48] A. Einstein, B. Podolsky, and N. Rosen, Physical Review 47, 777 (1935).
https://doi.org/10.1103/PhysRev.47.777

[49] E. Schrodinger, Mathematical Proceedings of the Cambridge Philosophical Society 31, 555 (1935).
https://doi.org/10.1017/S0305004100013554

[50] H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402 (2007).
https://doi.org/10.1103/PhysRevLett.98.140402

[51] P. Skrzypczyk, M. Navascués, and D. Cavalcanti, Physical Review Letters 112, 180404 (2014).
https://doi.org/10.1103/PhysRevLett.112.180404

[52] R. Gallego and L. Aolita, Physical Review X 5, 041008 (2015).
https://doi.org/10.1103/PhysRevX.5.041008

[53] M. Piani and J. Watrous, Physical Review Letters 114, 060404 (2015).
https://doi.org/10.1103/PhysRevLett.114.060404

[54] D. Cavalcanti and P. Skrzypczyk, Reports on Progress in Physics 80, 024001 (2017).
https://doi.org/10.1088/1361-6633/80/2/024001

[55] R. Uola, A. C. S. Costa, H. C. Nguyen, and O. Gühne, (2019), arXiv:1903.06663.
https://doi.org/10.1103/RevModPhys.92.015001
arXiv:1903.06663

[56] M. F. Pusey, Phys. Rev. A 88, 032313 (2013).
https://doi.org/10.1103/PhysRevA.88.032313

[57] D. Cavalcanti, P. Skrzypczyk, and I. Šupić, Phys. Rev. Lett. 119, 110501 (2017).
https://doi.org/10.1103/PhysRevLett.119.110501

[58] I. Šupić, P. Skrzypczyk, and D. Cavalcanti, Phys. Rev. A 99, 032334 (2019).
https://doi.org/10.1103/PhysRevA.99.032334

[59] J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, Physical Review A 71, 022101 (2005).
https://doi.org/10.1103/PhysRevA.71.022101

[60] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014b).
https://doi.org/10.1103/RevModPhys.86.419

[61] F. Buscemi, Phys. Rev. Lett. 108, 200401 (2012).
https://doi.org/10.1103/PhysRevLett.108.200401

[62] E. G. Cavalcanti, M. J. W. Hall, and H. M. Wiseman, Phys. Rev. A 87, 032306 (2013).
https://doi.org/10.1103/PhysRevA.87.032306

[63] M. Piani, J. Opt. Soc. Am. B 32, A1 (2015).
https://doi.org/10.1364/JOSAB.32.0000A1

[64] J. Henson, R. Lal, and M. F. Pusey, New J. Phys. 16, 113043 (2014).
https://doi.org/10.1088/1367-2630/16/11/113043

[65] A. B. S. John Selby, Paulo Cavalcanti, ``Extended boxworld: a generalised probabilistic theory for type independent common cause resources,'' Forthcoming.

[66] T. Eggeling, D. Schlingemann, and R. F. Werner, Europhysics Letters (EPL) 57, 782 (2002).
https://doi.org/10.1209/epl/i2002-00579-4

[67] P. Lipka-Bartosik and P. Skrzypczyk, (2019), arXiv:1908.05107.
https://doi.org/10.1103/PhysRevResearch.2.023029
arXiv:1908.05107

[68] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. Lett. 101, 060401 (2008).
https://doi.org/10.1103/PhysRevLett.101.060401

[69] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. A 80, 022339 (2009).
https://doi.org/10.1103/PhysRevA.80.022339

[70] V. Scarani, Bell Nonlocality (OUP, 2019).

[71] D. Rosset, F. Buscemi, and Y.-C. Liang, Phys. Rev. X 8, 021033 (2018).
https://doi.org/10.1103/PhysRevX.8.021033

[72] R. Takagi and B. Regula, Phys. Rev. X 9, 031053 (2019).
https://doi.org/10.1103/PhysRevX.9.031053

[73] R. Uola, T. Kraft, and A. A. Abbott, Phys. Rev. A 101, 052306 (2020).
https://doi.org/10.1103/PhysRevA.101.052306

[74] D. Schmid, T. C. Fraser, R. Kunjwal, A. B. Sainz, E. Wolfe, and R. W. Spekkens, ``Why standard entanglement theory is inappropriate for the study of bell scenarios,'' (2019b), arXiv:2004.09194 [quant-ph].
arXiv:2004.09194

[75] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
https://doi.org/10.1103/PhysRevLett.23.880

[76] C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
https://doi.org/10.1103/PhysRevA.59.1070

[77] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
https://doi.org/10.1103/PhysRevLett.70.1895

[78] Y. R. Sanders, Resource Theories in Quantum Information, Ph.D. thesis, University of Calgary (2012).
https://doi.org/10.11575/PRISM/3875

[79] T. Gonda and R. W. Spekkens, (2019), arXiv:1912.07085.
arXiv:1912.07085

Cited by

[1] Martin Plávala, "General probabilistic theories: An introduction", Physics Reports 1033, 1 (2023).

[2] Carolina Moreira Ferrera, Robin Simmons, James Purcell, Daniel Collins, and Sandu Popescu, "Classical-to-quantum non-signalling boxes", Quantum 8, 1443 (2024).

[3] Simon Milz, Jessica Bavaresco, and Giulio Chiribella, "Resource theory of causal connection", Quantum 6, 788 (2022).

[4] Edric Matwiejew, Pascal Elahi, and Ugo Varetto, 2026 IEEE 46th International Conference on Distributed Computing Systems Workshops (ICDCSW) 172 (2026) ISBN:979-8-3195-3647-1.

[5] David Schmid, Denis Rosset, and Francesco Buscemi, "The type-independent resource theory of local operations and shared randomness", Quantum 4, 262 (2020).

[6] Nitica Sakharwade, Michał Studziński, Michał Eckstein, and Paweł Horodecki, "Two instances of random access code in the quantum regime", New Journal of Physics 25 5, 053038 (2023).

[7] Albert Rico, Moisés Bermejo Morán, Fereshte Shahbeigi, and Karol Życzkowski, "Channel Nonlocality under Decoherence", Physical Review Letters 136 11, 110202 (2026).

[8] David Schmid, Thomas C. Fraser, Ravi Kunjwal, Ana Belen Sainz, Elie Wolfe, and Robert W. Spekkens, "Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory", Quantum 7, 1194 (2023).

[9] Ana Belén Sainz, Paul Skrzypczyk, and Matty J Hoban, "Activation of post-quantum steering", New Journal of Physics 27 12, 124508 (2025).

[10] Paulo J. Cavalcanti, John H. Selby, Jamie Sikora, Thomas D. Galley, and Ana Belén Sainz, "Post-quantum steering is a stronger-than-quantum resource for information processing", npj Quantum Information 8 1, 76 (2022).

[11] Paulo J. Cavalcanti, John H. Selby, and Ana Belén Sainz, "Every nonsignaling channel is common-cause realizable", Physical Review A 109 4, 042211 (2024).

[12] Matty J. Hoban, Tom Drescher, and Ana Belén Sainz, "A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios", Quantum 9, 1591 (2025).

[13] Gilad Gour and Carlo Maria Scandolo, "Entanglement of a bipartite channel", Physical Review A 103 6, 062422 (2021).

[14] Beata Zjawin, Matty J. Hoban, Paul Skrzypczyk, and Ana Belén Sainz, "Activation of postquantumness in bipartite generalized Einstein-Podolsky-Rosen scenarios", Physical Review A 110 4, 042212 (2024).

[15] Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes", Quantum 4, 280 (2020).

[16] Ian George and Eric Chitambar, "Reexamination of quantum state transformations with zero communication", Physical Review A 109 6, 062418 (2024).

[17] Patryk Lipka-Bartosik, Jessica Bavaresco, Nicolas Brunner, and Pavel Sekatski, "Power of quantum catalytic local operations", Physical Review A 113 6, 062216 (2026).

[18] Beata Zjawin, David Schmid, Matty J. Hoban, and Ana Belén Sainz, "Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages", Quantum 7, 926 (2023).

[19] Beata Zjawin, David Schmid, Matty J. Hoban, and Ana Belén Sainz, "The resource theory of nonclassicality of channel assemblages", Quantum 7, 1134 (2023).

[20] Albert Rico, Moisés Bermejo Morán, Fereshte Shahbeigi, and Karol Życzkowski, "Certifying nonlocal properties of noisy quantum operations", Quantum 9, 1807 (2025).

[21] Denis Rosset, David Schmid, and Francesco Buscemi, "Type-Independent Characterization of Spacelike Separated Resources", Physical Review Letters 125 21, 210402 (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 14:09:32) and SAO/NASA ADS (last updated successfully 2026-08-09 14:09:33). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.