Classical-to-quantum non-signalling boxes

Carolina Moreira Ferrera; Robin Simmons; James Purcell; Daniel Collins; Sandu Popescu

doi:10.22331/q-2024-08-22-1443

Classical-to-quantum non-signalling boxes

Carolina Moreira Ferrera¹, Robin Simmons², James Purcell³, Daniel Collins¹, and Sandu Popescu¹

¹H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL
²Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
³Dept. of Physics & Astronomy, University College London, WC1E 6BT, UK

Published:	2024-08-22, volume 8, page 1443
Eprint:	arXiv:2303.17268v6
Doi:	https://doi.org/10.22331/q-2024-08-22-1443
Citation:	Quantum 8, 1443 (2024).

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

Abstract

Here we introduce the concept of classical input – quantum output (C-Q) non-signalling boxes, a generalisation of the classical input – classical output (C-C) non-signalling boxes. We argue that studying such objects leads to a better understanding of the relation between quantum nonlocality and non-locality beyond quantum mechanics. The main issue discussed in the paper is whether there exist 'genuine' C-Q boxes or all C-Q boxes can be built from objects already known, namely C-C boxes acting on pre-shared entangled quantum particles. We show that large classes of C-Q boxes are non-genuine. In particular, we show that all bi-partite C-Q boxes with outputs that are pure states are non-genuine. We also present various strategies for addressing the general problem, i.e. for multi-partite C-Q boxes which output mixed states, whose answer is still open. Finally, we show that even some very simple non-genuine C-Q boxes require large amounts of C-C nonlocal correlations in order to simulate them.

Featured image: A CQ box with two parts, each of which takes a classical input, x and y respectively. It outputs a quantum state $\rho_{A,B}^{x,y}$, joint across A and B.

Popular summary

Non-locality is one of the most surprising and mysterious features of quantum physics. Experiments on a pair of distant quantum mechanical particles cannot be explained by classical relativistic physics, i.e. by classical physics which cannot send messages faster than the speed of light. Such experiments typically involve classical inputs and outputs, e.g. a choice of measurement on each particle and the results. Here we study a generalisation we call CQ boxes: experiments on distant particles which have classical inputs and which instead output a joint quantum state. We allow the particles to be governed by a post-quantum theory: one with outputs correlated more strongly than quantum mechanics, subject only to the constraint of no faster than light messages. The simpler case of post-quantum particles with classical inputs and classical outputs has already been studied extensively, and has brought significant insights in understanding non-locality, but cannot represent all the properties of ordinary quantum mechanics such as entanglement swapping. Our generalisation provides an even stronger tool for understanding non-locality in general, and may shed more light on what is specific to quantum mechanical non-locality.

► BibTeX data

@article{MoreiraFerrera2024classicaltoquantum,
  doi = {10.22331/q-2024-08-22-1443},
  url = {https://doi.org/10.22331/q-2024-08-22-1443},
  title = {Classical-to-quantum non-signalling boxes},
  author = {Moreira Ferrera, Carolina and Simmons, Robin and Purcell, James and Collins, Daniel and Popescu, Sandu},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1443},
  month = aug,
  year = {2024}
}

► References

[1] J. S. Bell. ``On the Einstein Podolsky Rosen paradox''. Physics 1, 195–200 (1964).
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195

[2] SJ Freedman and JF Clauser. ``Experimental test of local hidden-variable theories''. Phys. Rev. Lett. 28, 938–& (1972).
https://doi.org/10.1103/PhysRevLett.28.938

[3] A Aspect, P Grangier, and G Roger. ``Experimental tests of realistic local theories via Bell's theorem''. Phys. Rev. Lett. 47, 460–463 (1981).
https://doi.org/10.1103/PhysRevLett.47.460

[4] S Popescu and D Rohrlich. ``Quantum nonlocality as an axiom''. Found. Phys. 24, 379–385 (1994).
https://doi.org/10.1007/BF02058098

[5] J Barrett, N Linden, S Massar, S Pironio, S Popescu, and D Roberts. ``Nonlocal correlations as an information-theoretic resource''. Phys. Rev. A 71, 022101 (2005).
https://doi.org/10.1103/PhysRevA.71.022101

[6] Wim van Dam. ``Implausible consequences of superstrong nonlocality''. Nat. Comput. 12, 9–12 (2013).
https://doi.org/10.1007/s11047-012-9353-6

[7] G Brassard, H Buhrman, N Linden, AA Méthot, A Tapp, and F Unger. ``Limit on nonlocality in any world in which communication complexity is not trivial''. Phys. Rev. Lett. 96, 250401 (2006).
https://doi.org/10.1103/PhysRevLett.96.250401

[8] T. Fritz, A. B. Sainz, R. Augusiak, J. Bohr Brask, R. Chaves, A. Leverrier, and A. Acin. ``Local orthogonality as a multipartite principle for quantum correlations''. Nat. Commun. 4, 2263 (2013).
https://doi.org/10.1038/ncomms3263

[9] Miguel Navascues and Harald Wunderlich. ``A glance beyond the quantum model''. Proc. R. Soc. A 466, 881–890 (2010).
https://doi.org/10.1098/rspa.2009.0453

[10] Paul Skrzypczyk, Nicolas Brunner, and Sandu Popescu. ``Emergence of quantum correlations from nonlocality swapping''. Phys. Rev. Lett. 102, 110402 (2009).
https://doi.org/10.1103/PhysRevLett.102.110402

[11] Marcin Pawlowski, Tomasz Paterek, Dagomir Kaszlikowski, Valerio Scarani, Andreas Winter, and Marek Zukowski. ``Information causality as a physical principle''. Nature 461, 1101–1104 (2009).
https://doi.org/10.1038/nature08400

[12] Noah Linden, Sandu Popescu, Anthony J. Short, and Andreas Winter. ``Quantum nonlocality and beyond: Limits from nonlocal computation''. Phys. Rev. Lett. 99, 110402 (2007).
https://doi.org/10.1103/PhysRevLett.99.180502

[13] Matty J. Hoban and Ana Belen Sainz. ``A channel-based framework for steering, non-locality and beyond''. New J. Phys. 20, 053048 (2018).
https://doi.org/10.1088/1367-2630/aabea8

[14] Ana Belén Sainz, Nicolas Brunner, Daniel Cavalcanti, Paul Skrzypczyk, and Tamás Vértesi. ``Postquantum steering''. Phys. Rev. Lett. 115, 190403 (2015).
https://doi.org/10.1103/PhysRevLett.115.190403

[15] A. B. Sainz, L. Aolita, M. Piani, M. J. Hoban, and P. Skrzypczyk. ``A formalism for steering with local quantum measurements''. New J. Phys. 20, 083040 (2018).
https://doi.org/10.1088/1367-2630/aad8df

[16] Jonathan Barrett. ``Information processing in generalized probabilistic theories''. Phys. Rev. A 75, 032304 (2007).
https://doi.org/10.1103/PhysRevA.75.032304

[17] Lucien Hardy. ``Quantum theory from five reasonable axioms'' (2001). url: doi.org/10.48550/arXiv.quant-ph/0101012.
https://doi.org/10.48550/arXiv.quant-ph/0101012
arXiv:quant-ph/0101012

[18] Beata Zjawin, David Schmid, Matty J. Hoban, and Ana Belen Sainz. ``The resource theory of nonclassicality of channel assemblages''. Quantum 7, 1134 (2023).
https://doi.org/10.22331/q-2023-10-10-1134

[19] Martin Plavala. ``General probabilistic theories: An introduction''. Phys. Rep. 1033, 1–64 (2023).
https://doi.org/10.1016/j.physrep.2023.09.001

[20] A J Short, S Popescu, and N Gisin. ``Entanglement swapping for generalized nonlocal correlations''. Phys. Rev. A 73, 012101 (2006).
https://doi.org/10.1103/PhysRevA.73.012101

[21] Anthony J Short and Jonathan Barrett. ``Strong nonlocality: a trade-off between states and measurements''. New J. Phys. 12, 033034 (2010).
https://doi.org/10.1088/1367-2630/12/3/033034

[22] R Horodecki and M Horodecki. ``Information-theoretic aspects of inseparability of mixed states''. Phys. Rev. A 54, 1838–1843 (1996).
https://doi.org/10.1103/PhysRevA.54.1838

[23] Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine. ``Exact and approximate unitary 2-designs and their application to fidelity estimation''. Phys. Rev. A 80, 012304 (2009).
https://doi.org/10.1103/PhysRevA.80.012304

[24] CH Bennett, DP DiVincenzo, CA Fuchs, T Mor, E Rains, PW Shor, JA Smolin, and WK Wootters. ``Quantum nonlocality without entanglement''. Phys. Rev. A 59, 1070–1091 (1999).
https://doi.org/10.1103/PhysRevA.59.1070

[25] N Gisin and S Popescu. ``Spin flips and quantum information for antiparallel spins''. Phys. Rev. Lett. 83, 432–435 (1999).
https://doi.org/10.1103/PhysRevLett.83.432

[26] D Beckman, D Gottesman, MA Nielsen, and J Preskill. ``Causal and localizable quantum operations''. Phys. Rev. A 64, 052309 (2001).
https://doi.org/10.1103/PhysRevA.64.052309

[27] David Schmid, Haoxing Du, Maryam Mudassar, Ghi Coulter-de Wit, Denis Rosset, and Matty J. Hoban. ``Postquantum common-cause channels: the resource theory of local operations and shared entanglement''. Quantum 5, 419 (2021).
https://doi.org/10.22331/q-2021-03-23-419

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2026-08-08 23:17:04). On SAO/NASA ADS no data on citing works was found (last attempt 2026-08-08 23:17:04).

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.