Possibilistic and maximal indefinite causal order in the quantum switch

Tein van der Lugt; Nick Ormrod

doi:10.22331/q-2024-12-03-1543

Possibilistic and maximal indefinite causal order in the quantum switch

Tein van der Lugt¹ and Nick Ormrod^1,2

¹Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
²Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada

Published:	2024-12-03, volume 8, page 1543
Eprint:	arXiv:2311.00557v2
Doi:	https://doi.org/10.22331/q-2024-12-03-1543
Citation:	Quantum 8, 1543 (2024).

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Abstract

It was recently found that the indefinite causal order in the quantum switch can be certified device-independently when assuming the impossibility of superluminal influences. Here we strengthen this result in two ways. First, we give a proof of this fact which is possibilistic rather than probabilistic, i.e. which does not rely on the validity of probability theory at the hidden variable level. Then, returning to the probabilistic setting, we show that the indefinite causal order in the quantum switch is also maximal, in the sense that the observed correlations are incompatible even with the existence of a causal order on only a small fraction of the runs of the experiment. While the original result makes use of quantum theory's violation of a Clauser-Horne-Shimony-Holt inequality, the proofs presented here are based on Greenberger, Horne, and Zeilinger's and Mermin's proofs of nonlocality, respectively.

► BibTeX data

@article{vanderLugt2024possibilistic,
  doi = {10.22331/q-2024-12-03-1543},
  url = {https://doi.org/10.22331/q-2024-12-03-1543},
  title = {Possibilistic and maximal indefinite causal order in the quantum switch},
  author = {van der Lugt, Tein and Ormrod, Nick},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1543},
  month = dec,
  year = {2024}
}

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Cited by

[1] Veronika Baumann, Ämin Baumeler, and Eleftherios-Ermis Tselentis, "No quantum advantage for violating fixed-order inequalities?", New Journal of Physics 27 10, 104507 (2025).

[2] Anna Steffinlongo and Hippolyte Dourdent, "Simulating noncausality with quantum control of causal orders", Physical Review Research 8 1, 013127 (2026).

[3] Lee A. Rozema, Teodor Strömberg, Huan Cao, Yu Guo, Bi-Heng Liu, and Philip Walther, "Experimental aspects of indefinite causal order in quantum mechanics", Nature Reviews Physics 6 8, 483 (2024).

[4] Hippolyte Dourdent, Alastair A. Abbott, Ivan Šupić, and Cyril Branciard, "Network-Device-Independent Certification of Causal Nonseparability", Quantum 8, 1514 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-08 03:27:05) and SAO/NASA ADS (last updated successfully 2026-08-08 03:27:06). The list may be incomplete as not all publishers provide suitable and complete citation data.

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