Indefinite Causal Order and Quantum Coordinates

Author(s): Anne Catherine de la Hamette, Viktoria Kabel, Marios Christodoulou, Časlav Brukner
Abstract: Classically, the causal order of two timelike separated events A and B is fixed-either A before B or B before A. This is no longer true in quantum theory, where it is possible to encounter superpositions of causal orders. The quantum switch is one of the most prominent processes with indefinite causal order. Optical realizations of the quantum switch have been successfully implemented in experiments, but some argue that this merely simulates a process with indefinite causal order and that a superposition of spacetime metrics is required for a true realization. Here, we provide a relativistic definition of causal order between operationally defined events that defines a meaningful observable in both the general relativistic and quantum mechanical sense. Importantly, this observable does not distinguish between the indefinite causal order implemented on an optical bench and the gravitational quantum switch, a gedanken experiment where the indefinite causal order is achieved by a quantum superposition of gravitational fields. Therefore, our results support the thesis that the optical quantum switch is just as much a realization of indefinite causal order as its gravitational counterpart, which makes use of the quantum mechanical behavior of spacetime.
Organisation(s): Quantum Optics, Quantum Nanophysics and Quantum Information, Research Network Quantum Aspects of Space Time
External organisation(s): Österreichische Akademie der Wissenschaften (ÖAW)
Journal: Physical Review Letters
Volume: 135
No. of pages: 8
ISSN: 0031-9007
DOI: https://doi.org/10.48550/arXiv.2211.15685
Publication date: 10-2025
Peer reviewed: Yes
Austrian Fields of Science 2012: 103025 Quantum mechanics, 103028 Theory of relativity
ASJC Scopus subject areas: General Physics and Astronomy
Portal url: https://ucrisportal.univie.ac.at/en/publications/39c16739-43ba-41a6-841a-67fab39effcc