Circuit locality from relativistic locality in scalar field mediated entanglement
1Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
2Basic Research Community for Physics e.V., Mariannenstraße 89, Leipzig, Germany
3Physics Department, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK
4Quantum Group, Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom
5Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
6Research Platform TURIS, University of Vienna, Vienna, Austria
7Aix-Marseille University, Université de Toulon, CPT-CNRS, Marseille, France
8Department of Philosophy and the Rotman Institute of Philosophy, Western University, London ON, Canada
9Perimeter Institute, 31 Caroline Street N, Waterloo ON, Canada
| Published: | 2026-03-24, volume 10, page 2046 |
| Editor: | Luca Tagliacozzo |
| Eprint: | arXiv:2305.05645v4 |
| Doi: | https://doi.org/10.22331/q-2026-03-24-2046 |
| Citation: | Quantum 10, 2046 (2026). |
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Abstract
Locality is a central notion in modern physics, but different disciplines understand it in different ways. Quantum field theory focuses on relativistic locality, based on spacetime regions, while quantum information theory focuses circuit locality, based on the notion of subsystems. Here, we investigate how spacetime and subsystem locality are related in the context of systems getting entangled while interacting via a scalar field. We show how, when the systems are put in a quantum-controlled superposition of localised states, relativistic locality (in the form of microcausality) gives rise to a specific kind of circuit. The relation between these forms of locality is relevant for understanding whether it is possible to formulate quantum field theory in quantum circuit language, and has bearing on the recent discussions on low-energy tests of quantum gravity.
Featured image: Illustration of the main result of the paper, connecting spacetime locality (left) with circuit structure (right). Two particles $A$ and $B$, each coupled to a relativistic quantum scalar field $\phi$ are kept in a quantum-controlled superposition of localised trajectories. We show that, during each interval of time $(t_1,t_2)$ during which the particles remain in spacelike separation, the unitary $\hat U(t_1,t_2)$ that describes the evolution of the joint system decomposes into three unitaries: one that acts on the $\phi$ only and determines the evolution of its initial condition at $t_1$, one that acts only on $A$ and $\phi$ and encodes how $A$ and $\phi$ affect each other, and one that acts only on $B$ and $\phi$ and encodes how $B$ and $\phi$ affect each other. The evolution over longer intervals of time thus decompose in several rounds of such interaction and thus any information that is exchanged between $A$ and $B$—including that which is responsible for the generation of entanglement between them—is carried by the field.
Popular summary
Using approximations common in quantum optics and quantum information—where particles are in quantum-controlled superpositions of well-localised trajectories and we neglect the field’s effect on the trajectories—we can treat the field as evolving under effective classical sources in each branch of the quantum superposition. Solving this evolution exactly reveals a subtle phase term that is often neglected in standard treatments. This phase is crucial: it determines whether the interaction can be decomposed into operations local to the subsystems. When the particles are spacelike separated, microcausality (the vanishing of field commutators outside the lightcone) forces this phase to vanish. As a result, the full evolution factorises into a circuit where each gate in the circuit affects only the field and one particle at a time. Each round evolves the system for a finite time set by the spatial separation between the particles, making the role of spacetime locality explicit. The two particles can get entangled via the field only after at least rounds of this mediation evolution: once the circuit evolves the system long enough so that the trajectories come into causal contact.
Our results show that the notion of mediation used in quantum information–theoretic arguments can arise naturally from relativistic quantum field theory under physically-relevant conditions. A natural next step is to extend the analysis to general quantum sources and from scalar fields to gauge fields and ultimately to linearised quantum gravity.
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