Network-Device-Independent Certification of Causal Nonseparability

Hippolyte Dourdent; Alastair A. Abbott; Ivan Šupić; Cyril Branciard

doi:10.22331/q-2024-10-30-1514

Network-Device-Independent Certification of Causal Nonseparability

Hippolyte Dourdent¹, Alastair A. Abbott², Ivan Šupić³, and Cyril Branciard⁴

¹ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
²Univ. Grenoble Alpes, Inria, 38000 Grenoble, France
³LIP6, Sorbonne Université, CNRS, 4 Place Jussieu, 75005 Paris, France
⁴Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France

Published:	2024-10-30, volume 8, page 1514
Eprint:	arXiv:2308.12760v2
Doi:	https://doi.org/10.22331/q-2024-10-30-1514
Citation:	Quantum 8, 1514 (2024).

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Abstract

Causal nonseparability is the property underlying quantum processes incompatible with a definite causal order. So far it has remained a central open question as to whether any process with a clear physical realisation can violate a causal inequality, so that its causal nonseparability can be certified in a device-independent way, as originally conceived. Here we present a method solely based on the observed correlations, which certifies the causal nonseparability of all the processes that can induce a causally nonseparable distributed measurement in a scenario with trusted quantum input states, as defined in [Dourdent et al., Phys. Rev. Lett. 129, 090402 (2022)]. This notably includes the celebrated quantum switch. This device-independent certification is achieved by introducing a network of untrusted operations, allowing one to self-test the quantum inputs on which the effective distributed measurement induced by the process is performed.

Featured image: The Network-Device-Independent (NDI) scenario: Alice, Bob, Charlie and Daisy are given classical inputs $x,y,z,w$, and perform untrusted operations that produce outcomes $a,b,c,d$, resp. Verifying that the correlations $P_y(c,a|z,x)$ and $P_x(b,d|y,w)$ both maximally violate a Bell inequality allows one to self-test the preparation of Alice and Bob's quantum inputs; from this, one can certify the causal nonseparability of the distributed measurement $(\mathsf{E}_{a,b|x,y}^{\tilde{A}\tilde{B}})_{a,b}$ (purple semicircle) for specific $x$ and $y$, and thus the causal nonseparability of the process matrix $W^{AB}$ in a NDI scenario.

Popular summary

Quantum indeterminacy extends beyond physical properties like position or momentum – it can also apply to the causal order of local quantum operations. A key example is the “quantum switch”, a quantum process that uses a control qubit to apply two operations in a superposition of possible orders. Demonstration of this phenomenon, called causal nonseparability, in scenarios where the local devices cannot be trusted has been an open challenge. We present a method to certify it by using only observed correlations and a network of untrusted operations. This approach can be applied not only to the quantum switch, but also to any process that can be used to generate a so-called causally nonseparable distributed measurement.

► BibTeX data

@article{Dourdent2024networkdevice,
  doi = {10.22331/q-2024-10-30-1514},
  url = {https://doi.org/10.22331/q-2024-10-30-1514},
  title = {Network-{D}evice-{I}ndependent {C}ertification of {C}ausal {N}onseparability},
  author = {Dourdent, Hippolyte and Abbott, Alastair A. and {\v{S}}upi{\'{c}}, Ivan and Branciard, Cyril},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1514},
  month = oct,
  year = {2024}
}

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Cited by

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

[2] Dengke Qu, Quan Lin, Lei Xiao, Xiang Zhan, and Peng Xue, "Experimental violation of a Bell-like causal inequality in a photonic quantum switch", Science Advances 12 32, eaee9271 (2026).

[3] Tein van der Lugt and Nick Ormrod, "Possibilistic and maximal indefinite causal order in the quantum switch", Quantum 8, 1543 (2024).

[4] Yu Guo, Hao Tang, Bo-Xuan Wang, Min-Yu Lv, Jia-Wen Fan, Xiao-Min Hu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Giulio Chiribella, and Bi-Heng Liu, "Experimental violation of a Bell-like inequality for causal order", Science Advances 12 24, eaee2912 (2026).

[5] Matheus Capela and Kaumudibikash Goswami, "Entropic limitations on fixed causal order", Physical Review A 113 6, 062217 (2026).

[6] Matilde Baroni, Eleni Diamanti, Damian Markham, and Ivan Šupić, "Translating Bell nonlocality to prepare-and-measure scenarios under dimensional constraints", Physical Review A 112 6, 062220 (2025).

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

[8] Kuntal Sengupta, "Achieving Maximal Causal Indefiniteness in a Maximally Nonlocal Theory", arXiv:2411.04201, (2024).

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