- Featured in Physics
- Open Access
Toward an Experimental Device-Independent Verification of Indefinite Causal Order
PRX Quantum 7, 010354 – Published 17 March, 2026
DOI: https://doi.org/10.1103/5t2y-ddmt
Abstract
In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders—the so-called indefinite causal orders (ICOs)—which can provide operational advantages over classical scenarios. Verifying such phenomena has sparked significant interest, much like earlier efforts devoted to refuting local realism and confirming quantum entanglement. To date, demonstrations of ICO have all been based a process called the quantum switch and have relied on device-dependent or semi-device-independent protocols. Achieving a device-independent verification of ICO would imply that nature allows for correlations that do not respect causality, independent of any experimental assumptions or underlying theoretical description of the experiment. To this end, a recent theoretical development introduced a Bell-like inequality that allows for fully device-independent verification of ICO in a quantum switch. Here we implement this verification by experimentally violating this inequality. In particular, we measure a value of , which is 18 standard deviations above the definite causal order bound of . Our work presents the first implementation of a device-independent protocol to verify ICO, albeit in the presence of experimental loopholes. This represents an important step toward the device-independent verification of an ICO and provides a context in which to identify loopholes specifically related to the verification of ICO.
Physics Subject Headings (PhySH)
Research News
Can Before and After Be Superposed?
Through a quantum-switch experiment, researchers attempt to reveal “indefinite causal order”—a quantum phenomenon involving events in a before-and-after superposition.
See more in Physics
Popular Summary
Classical intuition dictates a strict order of cause and effect, but quantum theory suggests the possibility of “indefinite causal order” (ICO), where events can occur in a superposition of different temporal sequences. Demonstrating ICO has implications for fundamental physics and could lead to new quantum technologies.
Previous demonstrations of ICO relied on a process called the quantum switch, but required detailed knowledge of the devices used, making them device-dependent. In fact, it was thought that a fully device-independent verification of ICO could not be achieved with the quantum switch. Now, Richter et al. present an experiment that challenges this, taking a significant step toward device-independent verification. The team implemented a quantum switch, where the order of operations is entangled with the polarization of a second photon, and tested a recently developed Bell-like inequality that is violated only if ICO is present.
The experiment successfully violated the inequality, providing strong evidence for ICO using a quantum switch. While the experiment is not loophole-free (it does not eliminate all possible classical explanations), it represents an important advance. The result highlights the need for further research into loophole-free tests of ICO and opens new avenues for exploring the foundations of quantum mechanics and its potential to revolutionize information processing.
Article Text
Supplemental Material
References (58)
- O. Oreshkov, F. Costa, and Č. Brukner, Quantum correlations with no causal order, Nat. Commun. 3, 1092 (2012).
- G. Chiribella, G. M. D’Ariano, P. Perinotti, and B. Valiron, Quantum computations without definite causal structure, Phys. Rev. A 88, 022318 (2013).
- Ä. Baumeler, A. Feix, and S. Wolf, Maximal incompatibility of locally classical behavior and global causal order in multiparty scenarios, Phys. Rev. A 90, 042106 (2014).
- Ä. Baumeler and S. Wolf, The space of logically consistent classical processes without causal order, New J. Phys. 18, 013036 (2016).
- J. Wechs, H. Dourdent, A. A. Abbott, and C. Branciard, Quantum circuits with classical versus quantum control of causal order, PRX Quantum 2, 030335 (2021).
- C. Branciard, M. Araújo, A. Feix, F. Costa, and Č. Brukner, The simplest causal inequalities and their violation, New J. Phys. 18, 013008 (2016).
- G. Chiribella and Z. Liu, Quantum operations with indefinite time direction, Commun. Phys. 5, 190 (2022).
- L. A. Rozema, T. Strömberg, H. Cao, Y. Guo, B.-H. Liu, and P. Walther, Experimental aspects of indefinite causal order in quantum mechanics, Nat. Rev. Phys. 6, 483 (2024).
- L. M. Procopio, A. Moqanaki, M. Araújo, F. Costa, I. Alonso Calafell, E. G. Dowd, D. R. Hamel, L. A. Rozema, Č. Brukner, and P. Walther, Experimental superposition of orders of quantum gates, Nat. Commun. 6, 7913 (2015).
- G. Rubino, L. A. Rozema, A. Feix, M. Araújo, J. M. Zeuner, L. M. Procopio, Č. Brukner, and P. Walther, Experimental verification of an indefinite causal order, Sci. Adv. 3, e1602589 (2017).
- G. Rubino, L. A. Rozema, D. Ebler, H. Kristjánsson, S. Salek, P. Allard Guérin, A. A. Abbott, C. Branciard, Č. Brukner, G. Chiribella, and P. Walther, Experimental quantum communication enhancement by superposing trajectories, Phys. Rev. Res. 3, 013093 (2021).
- G. Rubino, L. A. Rozema, F. Massa, M. Araújo, M. Zych, Č. Brukner, and P. Walther, Experimental entanglement of temporal order, Quantum 6, 621 (2022).
- Y. Guo, X.-M. Hu, Z.-B. Hou, H. Cao, J.-M. Cui, B.-H. Liu, Y.-F. Huang, C.-F. Li, G.-C. Guo, and G. Chiribella, Experimental transmission of quantum information using a superposition of causal orders, Phys. Rev. Lett. 124, 030502 (2020).
- H. Cao, N.-N. Wang, Z. Jia, C. Zhang, Y. Guo, B.-H. Liu, Y.-F. Huang, C.-F. Li, and G.-C. Guo, Quantum simulation of indefinite causal order induced quantum refrigeration, Phys. Rev. Res. 4, L032029 (2022).
- H. Cao, J. Bavaresco, N.-N. Wang, L. A. Rozema, C. Zhang, Y.-F. Huang, B.-H. Liu, C.-F. Li, G.-C. Guo, and P. Walther, Semi-device-independent certification of indefinite causal order in a photonic quantum switch, Optica 10, 561 (2023).
- G. Zhu, Y. Chen, Y. Hasegawa, and P. Xue, Charging quantum batteries via indefinite causal order: Theory and experiment, Phys. Rev. Lett. 131, 240401 (2023).
- M. An, S. Ru, Y. Wang, Y. Yang, F. Wang, P. Zhang, and F. Li, Noisy quantum parameter estimation with indefinite causal order, Phys. Rev. A 109, 012603 (2024).
- K. Wei, N. Tischler, S.-R. Zhao, Y.-H. Li, J. M. Arrazola, Y. Liu, W. Zhang, H. Li, L. You, Z. Wang, Y.-A. Chen, B. C. Sanders, Q. Zhang, G. J. Pryde, F. Xu, and J.-W. Pan, Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity, Phys. Rev. Lett. 122, 120504 (2019).
- K. Goswami, C. Giarmatzi, M. Kewming, F. Costa, C. Branciard, J. Romero, and A. G. White, Indefinite causal order in a quantum switch, Phys. Rev. Lett. 121, 090503 (2018).
- K. Goswami, Y. Cao, G. A. Paz-Silva, J. Romero, and A. G. White, Increasing communication capacity via superposition of order, Phys. Rev. Res. 2, 033292 (2020).
- P. Yin, X. Zhao, Y. Yang, Y. Guo, W.-H. Zhang, G.-C. Li, Y.-J. Han, B.-H. Liu, J.-S. Xu, G. Chiribella et al., Experimental super-Heisenberg quantum metrology with indefinite gate order, Nat. Phys. 19, 1122 (2023).
- M. Antesberger, M. T. Quintino, P. Walther, and L. A. Rozema, Higher-order process matrix tomography of a passively-stable quantum switch, PRX Quantum 5, 010325 (2024).
- Y. Guo, Y. Chen, G. Chen, X.-M. Hu, Y.-F. Huang, C.-F. Li, G.-C. Guo, and B.-H. Liu, Surpassing the global Heisenberg limit using a high-effciency quantum switch, arXiv:2505.03290.
- M. Araújo, A. Feix, M. Navascués, and Č. Brukner, A purification postulate for quantum mechanics with indefinite causal order, Quantum 1, 10 (2017).
- T. Purves and A. J. Short, Quantum theory cannot violate a causal inequality, Phys. Rev. Lett. 127, 110402 (2021).
- J. Bavaresco, M. Murao, and M. T. Quintino, Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies, J. Math. Phys. 63, 042203 (2022).
- M. Araújo, F. Costa, and Č. Brukner, Computational advantage from quantum-controlled ordering of gates, Phys. Rev. Lett. 113, 250402 (2014).
- P. A. Guérin, A. Feix, M. Araújo, and Č. Brukner, Exponential communication complexity advantage from quantum superposition of the direction of communication, Phys. Rev. Lett. 117, 100502 (2016).
- D. Ebler, S. Salek, and G. Chiribella, Enhanced communication with the assistance of indefinite causal order, Phys. Rev. Lett. 120, 120502 (2018).
- D. Felce, V. Vedral, and F. Tennie, Refrigeration with indefinite causal orders on a cloud quantum computer, arXiv:2107.12413.
- T. Guha, M. Alimuddin, and P. Parashar, Thermodynamic advancement in the causally inseparable occurrence of thermal maps, Phys. Rev. A 102, 032215 (2020).
- K. Simonov, G. Francica, G. Guarnieri, and M. Paternostro, Work extraction from coherently activated maps via quantum switch, Phys. Rev. A 105, 032217 (2022).
- M. Frey, and Indefinite causal order aids quantum depolarizing channel identification, Quantum Inf. Process. 18, 96 (2019).
- H. Spencer-Wood, Indefinite causal key distribution, J. Phys. A: Math. Theor. 58, 495303 (2025).
- S. Koudia, A. S. Cacciapuoti, and M. Caleffi, Deterministic generation of multipartite entanglement via causal activation in the quantum internet, IEEE Access 11, 73863 (2023).
- I. Dey and N. Marchetti, Quantum teleportation in higher dimension and entanglement distribution via quantum switches, IET Quantum Commun. 6, e12122 (2025).
- L. K. Shalm et al., Strong loophole-free test of local realism, Phys. Rev. Lett. 115, 250402 (2015).
- M. Giustina et al., Significant-loophole-free test of Bell’s theorem with entangled photons, Phys. Rev. Lett. 115, 250401 (2015).
- B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature 526, 682 (2015).
- J.-P. W. Maclean, K. Ried, R. W. Spekkens, and K. J. Resch, Quantum-coherent mixtures of causal relations, Nat. Commun. 8, 15149 (2017).
- N. Ormrod, A. Vanrietvelde, and J. Barrett, Causal structure in the presence of sectorial constraints, with application to the quantum switch, Quantum 7, 1028 (2023).
- V. Vilasini and R. Renner, Embedding cyclic information-theoretic structures in acyclic space-times: No-go results for indefinite causality, Phys. Rev. A 110, 022227 (2024).
- N. Paunković and M. Vojinović, Causal orders, quantum circuits and spacetime: Distinguishing between definite and superposed causal orders, Quantum 4, 275 (2020).
- V. Vilasini, L.-Q. Chen, L. Ye, and R. Renner, Events and their localisation are relative to a lab, arXiv:2505.21797.
- T. van der Lugt, J. Barrett, and G. Chiribella, Device-independent certification of indefinite causal order in the quantum switch, Nat. Commun. 14, 5811 (2023).
- G. Luiz Zanin, M. J. Jacquet, M. Spagnolo, P. Schiansky, I. A. Calafell, L. A. Rozema, and P. Walther, Fiber-compatible photonic feed-forward with 99% fidelity, Opt. Express 29, 3425 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/5t2y-ddmt for a more detailed description of the setup and measurement methods, which includes Refs. [57, 58].
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, Cambridge, 2010), 10th ed., Chap. 8.3.3.
- M. M. Wilde, Quantum Information Theory (Cambridge University Press, 2017), pp. 155–156, Chap. 4.7.2.
- V. Scarani, Bell Nonlocality (Oxford University Press, Oxford, 2019), pp. 14–19.
- J. S. Bell and A. Aspect, in Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge University, Cambridge, 2004), pp. 243–244.
- O. Oreshkov, Time-delocalized quantum subsystems and operations: On the existence of processes with indefinite causal structure in quantum mechanics, Quantum 3, 206 (2019).
- G. Nogues, A. Rauschenbeutel, S. Osnaghi, M. Brune, J.-M. Raimond, and S. Haroche, Seeing a single photon without destroying it, Nature 400, 239 (1999).
- M. Zych, F. Costa, I. Pikovski, and Č. Brukner, Bell’s theorem for temporal order, Nat. Commun. 10, 1 (2019).
- A.-C. de la Hamette, V. Kabel, M. Christodoulou, and Č. Brukner, Indefinite causal order and quantum coordinates, Phys. Rev. Lett. 135, 141402 (2025).
- C. M. D. Richter, M. Antesberger, H. Cao, P. Walther, and L. Rozema, Towards an experimental device-independent verification of indefinite causal order, 2025, https://doi.org/10.5281/zenodo.15704777.
- G. L. Zanin, M. Antesberger, M. J. Jacquet, P. H. S. Ribeiro, L. A. Rozema, and P. Walther, Enhanced photonic Maxwell’s demon with correlated baths, Quantum 6, 810 (2022).
- G. L. Zanin, M. J. Jacquet, M. Spagnolo, P. Schiansky, I. A. Calafell, L. A. Rozema, and P. Walther, Fiber-compatible photonic feed-forward with 99% fidelity, Opt. Express 29, 3425 (2021).
