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Circuit locality from relativistic locality in scalar field mediated entanglement

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Circuit locality from relativistic locality in scalar field mediated entanglement

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AbstractLocality 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 summaryLocality is a central notion and guiding principle of theoretical physics. In relativistic quantum field theory, locality is expressed in spacetime terms: events outside each other’s light cones cannot influence one another. In quantum information theory, locality is instead described in terms of subsystems and quantum circuits: information can only flow through explicit interactions between systems. These notions clearly seem related but their precise relationship remains unclear. In particular, it is not obvious whether relativistic locality by itself implies the circuit-local structure assumed in quantum information theory. In this work we study a concrete example of how relativistic locality gives rise to the information-theoretic notion of locality. We consider two quantum systems that interact through a relativistic scalar field and show that, under physically realistic conditions, relativistic locality directly enforces a specific quantum-circuit structure for their evolution. In particular, when the systems are placed in quantum superpositions of spatially localised states and remain spacelike separated for finite periods of time, the dynamics takes the form of a sequence of operations in which each system interacts only with the field and never directly with the other system. In this sense, the field truly is the mediator for the interaction. 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.► BibTeX data@article{DiBiagio2026circuitlocalityfrom, doi = {10.22331/q-2026-03-24-2046}, url = {https://doi.org/10.22331/q-2026-03-24-2046}, title = {Circuit locality from relativistic locality in scalar field mediated entanglement}, author = {Di Biagio, Andrea and Howl, Richard and Brukner, {\v{C}}aslav and Rovelli, Carlo and Christodoulou, Marios}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2046}, month = mar, year = {2026} }► References [1] Anthony Duncan. ``The conceptual framework of quantum field theory''.

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Helvetica Physica Acta 23, 567–586 (1950). [38] Andrea Di Biagio. ``The simple reason why classical gravity can entangle'' (2025). arXiv:2511.02683. arXiv:2511.02683Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-24 16:30:02: Could not fetch cited-by data for 10.22331/q-2026-03-24-2046 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-24 16:30:03: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractLocality 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 summaryLocality is a central notion and guiding principle of theoretical physics. In relativistic quantum field theory, locality is expressed in spacetime terms: events outside each other’s light cones cannot influence one another. In quantum information theory, locality is instead described in terms of subsystems and quantum circuits: information can only flow through explicit interactions between systems. These notions clearly seem related but their precise relationship remains unclear. In particular, it is not obvious whether relativistic locality by itself implies the circuit-local structure assumed in quantum information theory. In this work we study a concrete example of how relativistic locality gives rise to the information-theoretic notion of locality. We consider two quantum systems that interact through a relativistic scalar field and show that, under physically realistic conditions, relativistic locality directly enforces a specific quantum-circuit structure for their evolution. In particular, when the systems are placed in quantum superpositions of spatially localised states and remain spacelike separated for finite periods of time, the dynamics takes the form of a sequence of operations in which each system interacts only with the field and never directly with the other system. In this sense, the field truly is the mediator for the interaction. 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.► BibTeX data@article{DiBiagio2026circuitlocalityfrom, doi = {10.22331/q-2026-03-24-2046}, url = {https://doi.org/10.22331/q-2026-03-24-2046}, title = {Circuit locality from relativistic locality in scalar field mediated entanglement}, author = {Di Biagio, Andrea and Howl, Richard and Brukner, {\v{C}}aslav and Rovelli, Carlo and Christodoulou, Marios}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2046}, month = mar, year = {2026} }► References [1] Anthony Duncan. ``The conceptual framework of quantum field theory''.

Oxford University Press. Oxford ; New York (2002). https://doi.org/10.1093/acprof:os0/9780199213900.001.0001 [22] Marlan O. Scully and M. Suhail Zubairy. ``Quantum Optics''.

The Advanced Book Program. CRC Press, Taylor & Francis Group.

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Circuit locality from relativistic locality in scalar field mediated entanglement

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