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arXiv:2604.11897

Particle detector in a position-superposed black hole spacetime

Laurens Walleghem, Carlo Cepollaro

quant-phgr-qchep-thSubmitted Apr 13, 2026• Announced Apr 15, 2026• Revised Sep 7, 2026 (v2)
v1 · Apr 13, 2026v2 · Sep 7, 2026
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Abstract

We calculate the response of an Unruh--DeWitt detector in a 2+1d spacetime that contains a BTZ black hole in a superposition of locations as viewed in a reference system associated with the detector. Upon performing a Quantum Reference Frame (QRF) transformation, this can also be seen as a detector in a superposition of locations in a single classical black hole spacetime. We use this to derive the form of the interaction of the detector and scalar field in such a superposition of spacetimes, ignoring backreaction. We define a measurement whose outcome probabilities contain a nonclassical contribution that would be absent for a black hole described by a classical mixture of positions. Finally, we compare our results with a previously studied setup involving a mass-superposed black hole by Foo et al. [Phys. Rev. Lett. 129, 181301 (2022)], and highlight a key difference. We show analytically how this difference arises and find singularities in the mass-superposed spectrum probed by the detector.

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We calculate the response of an Unruh--DeWitt detector in a 2+1d spacetime that contains a BTZ black hole in a superposition of locations as viewed in a reference system associated with the detector. Upon performing a Quantum Reference Frame (QRF) transformation, this can also be seen as a detector in a superposition of locations in a single classical black hole spacetime. We use this to derive the form of the interaction of the detector and scalar field in such a superposition of spacetimes, ignoring backreaction. We define a measurement whose outcome probabilities contain a nonclassical contribution that would be absent for a black hole described by a classical mixture of positions. Finally, we compare our results with a previously studied setup involving a mass-superposed black hole by Foo et al. [Phys. Rev. Lett. 129, 181301 (2022)], and highlight a key difference. We show analytically how this difference arises and find singularities in the mass-superposed spectrum probed by the detector.
Unruh-deWitt detectors have been utilized widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector traveling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as nonlocally between the superposed trajectories. By applying our general approach to a detector traveling in a superposition of two uniformly accelerated trajectories, including those with equal and differing proper accelerations, we discover novel interference effects in the emission and absorption spectra. These effects can be traced to causal relations between the superposed trajectories. Finally, we show that in general, such a detector does not thermalize even if the superposed paths would individually yield the same thermal state.
The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames used, explicitly or implicitly, in our description of physical systems. Like classical reference frames, QRFs can be used to define physical quantities relationally. Unlike their classical analogue, they relativise the notions of superposition and entanglement. Here, we explain this feature by examining how configurations or locations are identified across different branches in superposition. We show that, in the presence of symmetries, whether a system is in "the same" or "different" configurations across the branches depends on the choice of QRF. Hence, sameness and difference - and thus superposition and entanglement - lose their absolute meaning. We apply these ideas to the context of semi-classical spacetimes in superposition and use coincidences of four scalar fields to construct a comparison map between spacetime points in the different branches. This reveals that the localisation of an event is frame-dependent. We discuss the implications for indefinite causal order and the locality of interaction and conclude with a generalisation of Einstein's hole argument to the quantum context.
A bstract In this paper, we explore correlation harvesting in quantum superposition, specifically focusing on the entanglement and mutual information extracted by two Unruh-DeWitt detectors interacting with a quantum field in a mass-superposed BTZ black hole spacetime. Our findings reveal that the superposed nature of spacetime induces constructive interference between the field modes that can significantly enhance the entanglement harvesting relative to a single spacetime background. In contrast to entanglement, the mutual information obtained in spacetime superposition is influenced by the proper distance between the two detectors. While the mutual information harvested in a superposed spacetime remains lower than that in a single spacetime when the proper distance between detectors is small, it exceeds that in a single spacetime for specific mass ratios as the distance increases. Notably, we find that both entanglement and mutual information harvesting reach their maxima when the final spacetime superposition state is conditioned to align with the initial spacetime state.
In their strongest usage, quantum reference frames have been described as referring to "the measurements performed by a superposed lab", "the perspective of a quantum particle", "the point of view of a superposed observer", etc. While exciting, these operational proposals have remained brief and ambiguous, leading to misinterpretations and criticism. Here, we provide a detailed specification and defense of the notion of a position-superposed lab or observer. We argue that this requires no exotic claims about quantum physics and raises no greater interpretive difficulty than ordinary quantum measurements. We then derive several consequences of taking this operational meaning seriously. We stress that the position-superposed observers that define quantum references frames are different from, and considerably less problematic than, the outcome-superposed observers considered in Wigners' friend scenarios. In particular, we show that outcomes obtained by a position-superposed observer may (without decohering the superposition) be broadcast to a well-localised one, in contrast with Wigner's friend scenarios, which require the outcomes to remain internal to the system at hand. Finally, we defend the possibility to roleplay a quantum reference frame from a classical reference frame.
Hawking radiation is the proposed thermal black-body radiation of quantum nature emitted from a black hole. One common way to give an account of Hawking radiation is to consider a detector that follows a static trajectory in the vicinity of a black hole and interacts with the quantum field of the radiation. In the present work, we study the Hawking radiation perceived by a detector that follows a quantum superposition of static trajectories in Schwarzschild spacetime, instead of a unique well-defined trajectory. We analyze the quantum state of the detector after the interaction with a massless real scalar field. We find that for certain trajectories and excitation levels, there are nonvanishing coherences in the final state of the detector. We then examine the dependence of these coherences on the trajectories followed by the detector and relate them to the distinguishability of the different possible states in which the field is left after the excitation of the detector. We interpret our results in terms of the spatial distribution and propagation of particles of the quantum field.
Abstract As a combination of the microscopic structure of spacetime and the principle of quantum superposition, the study of spacetime superposition provides a fundamental bottom-up approach to a comprehensive understanding of relativity and quantum theory. In this paper, we study how quantum gravitational effects generated by the superposition of the black hole’s masses affect the many-body entanglement for Dirac fields. The main obstacle to performing quantum information processing tasks near a classical black hole is the inevitable entanglement degradation caused by the Unruh–Hawking thermal bath. Fortunately, here we find that the many-body quantum system near a black hole with superposing masses exhibits more entanglement compared to those in the classical black hole background. The superposition properties of spacetime are found to provide additional quantum resources for mitigating gravitationally induced quantum decoherence and improving the efficiency of quantum information tasks in curved spacetime. In addition, the greatest quantum advantage for the recovery of entanglement in the curved spacetime can be obtained by preparing an optimal initial state.