- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Factorization conditions and causality for local measurements in QFT

Robin Simmons1,2, Maria Papageorgiou2, Marios Christodoulou2, and Časlav Brukner1,2

PDF

Phys. Rev. D 114, 085013 – Published 15 October, 2026

DOI: https://doi.org/10.1103/sxkx-sy9g

Abstract

Quantum operations that are perfectly admissible in nonrelativistic quantum theory can enable signaling between spacelike separated regions when naively imported into quantum field theory (QFT). Prominent examples of such “impossible measurements” include certain unitary kicks and projective measurements. It is generally accepted that only those quantum operations whose physical implementation arises from a fully relativistically covariant interaction, between the quantum field and a suitable probe, should be regarded as admissible. While this idea has been realized at the level of abstract algebraic QFT, or via particular measurement models, there is still no general set of operational criteria characterizing which measurements are physically implementable. In this work we adopt the local S-matrix formalism to describe local operations, and make use of a hierarchy of factorization conditions that exclude both superluminal signaling and retrocausality, thereby providing such a criterion. Realizing the local S-matrices through explicit interactions between smeared field operators and a pointer degree of freedom, we further derive local causality conditions for the induced Kraus operators, which guarantee the absence of signaling in “impossible measurement” scenarios. Finally, we show that the accuracy with which local field observables can be measured is fundamentally limited by the retarded propagator of the field, which plays an essential role in the factorization identity we prove for the field Kraus operators.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (52)

  1. R. D. Sorkin, Impossible measurements on quantum fields, in Directions in General Relativity: Proceedings of the 1993 International Symposium, Maryland (Cambridge University Press, Cambridge, England, 1993), Vol. 2, pp. 293–305, arXiv:gr-qc/9302018.
  2. M. Papageorgiou and D. Fraser, Eliminating the ’impossible’: Recent progress on local measurement theory for quantum field theory, Found. Phys. 54, 1 (2024).
  3. D. Fraser and M. Papageorgiou, Note on episodes in the history of modeling measurements in local spacetime regions using QFT, Eur. Phys. J. H 48, 14 (2023).
  4. L. Borsten, I. Jubb, and G. Kells, Impossible measurements revisited, Phys. Rev. D 104, 025012 (2021).
  5. D. M. T. Benincasa, L. Borsten, M. Buck, and F. Dowker, Quantum information processing and relativistic quantum fields, Classical Quantum Gravity 31, 075007 (2014).
  6. E. Albertini and I. Jubb, Are ideal measurements of real scalar fields causal?, arXiv:2306.12980.
  7. I. Jubb, Causal state updates in real scalar quantum field theory, Phys. Rev. D 105, 025003 (2022).
  8. N. Gisin and F. Del Santo, Towards a measurement theory in QFT: “Impossible” quantum measurements are possible but not ideal, Quantum 8, 1267 (2024).
  9. R. Oeckl, Spectral decomposition of field operators and causal measurement in quantum field theory, J. Math. Phys. (N.Y.) 66, 042302 (2025).
  10. J. Mandrysch and M. Navascués, Quantum field measurements in the Fewster–Verch framework, Lett. Math. Phys. 115 (2025).
  11. C. J. Fewster and R. Verch, Quantum fields and local measurements, Commun. Math. Phys. 378, 851 (2020).
  12. H. Bostelmann, C. J. Fewster, and M. H. Ruep, Impossible measurements require impossible apparatus, Phys. Rev. D 103, 025017 (2021).
  13. C. J. Fewster, I. Jubb, and M. H. Ruep, Asymptotic measurement schemes for every observable of a quantum field theory, Ann. Henri Poincaré 24, 1137 (2023).
  14. N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields (Interscience Publishers, Inc., New York, 1959).
  15. A. S. Blum and J. D. Fraser, Perturbative causality, Synthese 206, 70 (2025).
  16. H. Epstein and V. Glaser, The role of locality in perturbation theory, Ann. Inst. Henri Poincare Phys. Theor. A 19, 211 (1973), https://www.numdam.org/item/AIHPA_1973__19_3_211_0/.
  17. K. Rejzner, Perturbative Algebraic Quantum Field Theory: An Introduction for Mathematicians, Mathematical Physics Studies (Springer, New York, 2016).
  18. D. Buchholz and K. Fredenhagen, A C*-algebraic approach to interacting quantum field theories, Commun. Math. Phys. 377, 947 (2020).
  19. M. Papageorgiou, J. de Ramón, and C. Anastopoulos, Particle-field duality in QFT measurements, Phys. Rev. D 109, 065024 (2024).
  20. K. Hellwig and K. Kraus, Operations and measurements. II, Commun. Math. Phys. 16, 142 (1970).
  21. P. Busch, P. Lahti, J.-P. Pellonpää, and K. Ylinen, Quantum Measurement, Theoretical and Mathematical Physics (Springer International Publishing, New York, 2016).
  22. P. Busch and P. Lahti, The standard model of quantum measurement theory: History and applications, Found. Phys. 26, 875 (1996).
  23. C. J. Fewster and K. Rejzner, Algebraic quantum field theory—an introduction, arXiv:1904.04051.
  24. H. J. Borchers and J. Yngvason, From quantum fields to local von Neumann algebras, Rev. Math. Phys. 04, 15 (1992).
  25. R. Haag and D. Kastler, An algebraic approach to quantum field theory, J. Math. Phys. (N.Y.) 5, 848 (1964).
  26. J. Earman and G. Valente, Relativistic causality in algebraic quantum field theory, Int. Stud. Philos. Sci. 28, 1 (2014).
  27. L. Ruetsche, Locality in (axiomatic) quantum field theory: A minority report, in Routledge Companion to Philosophy of Physics, edited by E. Knox and A. Wilson (Routledge, London and New York, 2021).
  28. F. Calderón, The causal axioms of algebraic quantum field theory: A diagnostic, Studies in history and philosophy of science 104, 98 (2024).
  29. A. Soulas, A proof that no-signalling implies microcausality in quantum field theory, Found. Phys. 55, 22 (2025).
  30. M. Rédei and G. Valente, How local are local operations in local quantum field theory?, Stud. Hist. Phil. Sci. Part B 41, 346 (2010).
  31. A. Holevo, Quantum Systems, Channels, Information: A Mathematical Introduction, Texts and Monographs in Theoretical Physics (Walter de Gruyter GmbH, Berlin/Boston, 2019).
  32. J. de Ramón, M. Papageorgiou, and E. Martín-Martínez, Relativistic causality in particle detector models: Faster-than-light signaling and impossible measurements, Phys. Rev. D 103, 085002 (2021).
  33. K. Rejzner, Locality and causality in perturbative AQFT, J. Math. Phys. (N.Y.) 60, 122301 (2019).
  34. J. D. Fraser and K. Rejzner, Perturbative expansions and the foundations of quantum field theory, Eur. Phys. J. H 49, 10 (2024).
  35. R. Brunetti and K. Fredenhagen, Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds, Commun. Math. Phys. 208, 623 (2000).
  36. J. Polo-Gómez, L. J. Garay, and E. Martín-Martínez, A detector-based measurement theory for quantum field theory, Phys. Rev. D 105, 065003 (2022).
  37. M. H. Ruep, Causality and measurement in quantum field theory on fixed backgrounds, Ph.D. thesis, University of York, 2022.
  38. B. Chilian and K. Fredenhagen, The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes, Commun. Math. Phys. 287, 513 (2009).
  39. A. Much and R. Verch, Superluminal local operations in quantum field theory: A ping-pong ball test, Universe 9, 447 (2023).
  40. K. Hellwig and K. Kraus, Pure operations and measurements, Commun. Math. Phys. 11, 214 (1969).
  41. A. R. Smith, Detectors, reference frames, and time, Ph.D. thesis, University of Waterloo, 2017.
  42. G. C. Hegerfeldt, Particle localization and the notion of Einstein causality, arXiv:quant-ph/0109044.
  43. D. B. Malament, In defense of dogma: Why there cannot be a relativistic quantum mechanics of (localizable) particles, in Perspectives on Quantum Reality (Springer, New York, 1996), pp. 1–10.
  44. M. Ozawa, Canonical approximate quantum measurements, J. Math. Phys. (N.Y.) 34, 5596 (1993).
  45. R. Oeckl, Causal measurement in quantum field theory: Spacetime, Phys. Rev. D 113, 085002 (2026).
  46. R. Oeckl and A. Zampeli, Towards local and compositional measurements in quantum field theory, arXiv:2505.10968.
  47. L. Vaidman, Instantaneous measurement of nonlocal variables, Phys. Rev. Lett. 90, 010402 (2003).
  48. S. Popescu and L. Vaidman, Causality constraints on nonlocal quantum measurements, Phys. Rev. A 49, 4331 (1994).
  49. J. Fuksa, Limits on relativistic quantum measurement, arXiv:2109.03187.
  50. R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (University of Chicago Press, Chicago, 1994).
  51. J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128, 183 (1972).
  52. C. J. Fewster, Modified Green-hyperbolic operators, SIGMA 19, 057 (2023).

Outline

Information

Phys. Rev. D 114, 085013– Published 15 October, 2026
  • Received 4 February 2026
  • Accepted 24 September 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation