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Experimental aspects of indefinite causal order in quantum mechanics

Nature Reviews Physics volume 6, pages 483–499 (2024)Cite this article

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Abstract

In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics and general relativity, these causally indefinite processes have been shown to offer advantages in a wide variety of quantum-information processing tasks, ranging from quantum computation to quantum metrology. Here, we overview these advantages and the experimental efforts to realize them. We survey both the experimental techniques employed and the theoretical methods developed in support of the experiments, before discussing the interpretations of current experimental results and giving an outlook on the future of the field.

Key points

  • An indefinite causal order (ICO) is a situation wherein the order of different events or operations is placed in a quantum superposition. Thus one cannot ascribe a definite order to these operations.

  • The best-studied process with an ICO is the quantum switch, which applies a set of quantum gates in a superposition of all possible permutations. The quantum switch has been experimentally implemented using various degrees of freedom encoded in single photons.

  • There is a strong analogy between processes with an ICO and entangled states. This analogy can be used to design techniques to certify ICO.

  • The quantum switch can be used to achieve advantages that go beyond devices that can be described by the quantum circuit model. Although there is no general computational advantage from the quantum switch, there are many specific applications, including quantum computation protocols, quantum communication, quantum metrology and even quantum thermodynamics.

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Fig. 1: Different control state encodings to realize the quantum switch.
Fig. 2: Certification of indefinite causal order.
Fig. 3: Experimental applications of indefinite causal order processes.
Fig. 4: Experimental loopholes.

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Acknowledgements

This research was funded in whole, or in part, by the European Union (ERC, GRAVITES, no. 101071779) and its Horizon 2020 and Horizon Europe Research and Innovation Programme under grant agreement no. 899368 (EPIQUS) and no. 101135288 (EPIQUE) and the Marie Skłodowska-Curie grant agreement no. 956071 (AppQInfo). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. Further funding was received from the Austrian Science Fund (FWF) through 10.55776/COE1 (Quantum Science Austria), 10.55776/F71 (BeyondC) and 10.55776/FG5 (Research Group 5) and from the Air Force Office of Scientific Research under award number FA9550-21-1-0355 (QTRUST) and FA8655-23-1-7063 (TIQI); the financial support by the Austrian Federal Ministry of Labour and Economy, the National Foundation for Research, Technology and Development and the Christian Doppler Research Association is gratefully acknowledged. L.A.R. acknowledges support from the Erwin Schrödinger Center for Quantum Science and Technology (ESQ Discovery). B.-H.L. and Y.G. were supported by NSFC (no. 12374338 and no. 12204458) and China Postdoctoral Science Foundation (2021M700138 and BX2021289). This work benefitted from network activities through the INAQT network, supported by the Engineering and Physical Sciences Research Council (grant no. EP/W026910/1).

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  1. These authors contributed equally: Lee A. Rozema, Teodor Strömberg, Huan Cao, Yu Guo.

Authors and Affiliations

  1. Faculty of Physics, University of Vienna, Vienna Center for Quantum Science and Technology (VCQ), Vienna, Austria

    Lee A. Rozema, Teodor Strömberg, Huan Cao & Philip Walther

  2. Research Platform for Testing the Quantum Gravity Interface (TURIS), University of Vienna, Vienna, Austria

    Lee A. Rozema, Teodor Strömberg, Huan Cao & Philip Walther

  3. CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, China

    Yu Guo & Bi-Heng Liu

  4. CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China

    Yu Guo & Bi-Heng Liu

  5. Hefei National Laboratory, University of Science and Technology of China, Hefei, China

    Bi-Heng Liu

  6. Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, Austria

    Philip Walther

  7. Christian Doppler Laboratory for Photonic Quantum Computer, University of Vienna, Vienna, Austria

    Philip Walther

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Rozema, L.A., Strömberg, T., Cao, H. et al. Experimental aspects of indefinite causal order in quantum mechanics. Nat Rev Phys 6, 483–499 (2024). https://doi.org/10.1038/s42254-024-00739-8

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