Superpositions of thermalisations in relativistic quantum field theory

Joshua Foo; Magdalena Zych

doi:10.22331/q-2025-02-11-1629

Superpositions of thermalisations in relativistic quantum field theory

Joshua Foo^1,2,3 and Magdalena Zych^4,5

¹Centre for Quantum Computation & Communication Technology, School of Mathematics & Physics, The University of Queensland, St. Lucia, Queensland, 4072, Australia
²Department of Physics, Stevens Institute of Technology, Castle Point Terrace, Hoboken, New Jersey 07030, U.S.A.
³Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
⁴Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland, 4072, Australia
⁵Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden

Published:	2025-02-11, volume 9, page 1629
Editor:	Mark Mitchison
Eprint:	arXiv:2307.02593v2
Doi:	https://doi.org/10.22331/q-2025-02-11-1629
Citation:	Quantum 9, 1629 (2025).

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Abstract

Recent results in relativistic quantum information and quantum thermodynamics have independently shown that in the quantum regime, a system may fail to thermalise when subject to quantum-controlled application of the same, single thermalisation channel. For example, an accelerating system with fixed proper acceleration is known to thermalise to an acceleration-dependent temperature, known as the Unruh temperature. However, the same system in a superposition of spatially translated trajectories that share the same proper acceleration fails to thermalise. Here, we provide an explanation of these results using the framework of quantum field theory in relativistic noninertial reference frames. We show how a probe that accelerates in a superposition of spatial translations interacts with incommensurate sets of field modes. In special cases where the modes are orthogonal (for example, when the Rindler wedges are translated in a direction orthogonal to the plane of motion), thermalisation does indeed result, corroborating the here provided explanation. We then discuss how this description relates to an information-theoretic approach aimed at studying quantum aspects of temperature through quantum-controlled thermalisations. The present work draws a connection between research in quantum information, relativistic physics, and quantum thermodynamics, in particular showing that relativistic quantum effects can provide a natural realisation of quantum thermodynamical scenarios.

Featured image: Superpositions of relativistic noninertial observers in Rindler and diamond coordinates respectively. In our work, we consider the "temperature" such observers detect when interacting with a quantum field.

Popular summary

A foundational question at the interface of quantum theory and thermodynamics is the notion of temperature for delocalised systems. It has been shown that a quantum system in superposition may fail to thermalise to the temperature of its environment, even when each branch is subject to the same, single thermalisation channel. Here, we elucidate the reason for such behaviour using tools from quantum field theory in noninertial reference frames. When an observer or probe in superposition interacts with different sets of correlated field modes—such as those in spatially translated Rindler wedges—interference between them results in a deviation from the expected thermal spectrum. Our work connects research in quantum information, spacetime physics, and quantum thermodynamics, in particular showing that relativistic quantum effects can provide a natural realisation of interesting quantum thermodynamical scenarios.

► BibTeX data

@article{Foo2025superpositionsof,
  doi = {10.22331/q-2025-02-11-1629},
  url = {https://doi.org/10.22331/q-2025-02-11-1629},
  title = {Superpositions of thermalisations in relativistic quantum field theory},
  author = {Foo, Joshua and Zych, Magdalena},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1629},
  month = feb,
  year = {2025}
}

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