Operational theory for photonic circuits: generalizing linear optics beyond quantum theory

Abstract

We use the analogy between the quadrature operators in quantum optics and the phase-space coordinates in a mechanical harmonic oscillator to generalise the theory of linear optics beyond quantum theory. For this, we introduce a framework for analysing photonic circuits within generalised probabilistic theories based on quadrature operators. Using this framework, we ask whether phenomena like the Hong-Ou-Mandel effect, Mach-Zehnder interferometry are specific to quantum theory or also occur across a broader class of theories. We find the latter: the vanishing photon coincidences at the output of a beam splitter also occur for classical light and for a modified version of quantised light. Similarly, for Mach-Zehnder interferometry we find that there is no qualitative difference between quantum theory and these alternative theories. Our framework can serve as a foundation to study generalised theories of complex photonic set-ups and photonic quantum computers.

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BibTeX

@misc{septembre2026operational,
  title = {{Operational theory for photonic circuits: generalizing linear optics beyond quantum theory}},
  author = {Ismaël Septembre and Matthias Kleinmann and Martin Plávala},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37628},
  eprint = {2609.37628},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37628},
}

RIS

TY  - UNPB
TI  - Operational theory for photonic circuits: generalizing linear optics beyond quantum theory
AU  - Ismaël Septembre
AU  - Matthias Kleinmann
AU  - Martin Plávala
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37628
UR  - https://arxiv.org/abs/2609.37628
AB  - We use the analogy between the quadrature operators in quantum optics and the phase-space coordinates in a mechanical harmonic oscillator to generalise the theory of linear optics beyond quantum theory. For this, we introduce a framework for analysing photonic circuits within generalised probabilistic theories based on quadrature operators. Using this framework, we ask whether phenomena like the Hong-Ou-Mandel effect, Mach-Zehnder interferometry are specific to quantum theory or also occur across a broader class of theories. We find the latter: the vanishing photon coincidences at the output of a beam splitter also occur for classical light and for a modified version of quantised light. Similarly, for Mach-Zehnder interferometry we find that there is no qualitative difference between quantum theory and these alternative theories. Our framework can serve as a foundation to study generalised theories of complex photonic set-ups and photonic quantum computers.
ER  -

Abstract

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