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arXiv:2607.19763

Energy Flux as an Entanglement Current in Moving-Mirror Radiation

Yasusada Nambu, Riku Yoshimoto

gr-qchep-thquant-phSubmitted Jul 22, 2026• Announced Jul 23, 2026• 0 citations• Revised Aug 6, 2026 (v3)
v1 · Jul 22, 2026v2 · Jul 27, 2026v3 · Aug 6, 2026
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Abstract

In this work, we investigate the quantum entanglement properties of analog Hawking radiation produced by a moving mirror. Using two detector modes defined through window functions on a quantum field, we quantify the bipartite entanglement established between these modes. Our results reveal that the amount of entanglement accessible to the detectors increases when the mirror follows trajectories with non-monotonic, time-dependent acceleration, which are accompanied by the emission of negative energy flux. This indicates that the negative energy flux acts as a channel through which information can be returned. To substantiate this perspective, we examine how the recovery or reconstruction of the associated partner modes is related to the negative energy flux emitted by the mirror.

Comments
21 pages, 11 figures

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In this work, we investigate the quantum entanglement properties of analog Hawking radiation produced by a moving mirror. Using two detector modes defined through window functions on a quantum field, we quantify the bipartite entanglement established between these modes. Our results reveal that the amount of entanglement accessible to the detectors increases when the mirror follows trajectories with non-monotonic, time-dependent acceleration, which are accompanied by the emission of negative energy flux. This indicates that the negative energy flux acts as a channel through which information can be returned. To substantiate this perspective, we examine how the recovery or reconstruction of the associated partner modes is related to the negative energy flux emitted by the mirror.
We examine the condition necessary for extracting entanglement from a quantum field through the use of two local modes A and B (detector modes). We show that Simon's entanglement criterion for the bipartite Gaussian state can be reformulated in terms of commutators between the canonical operators of the detector mode B and the partner mode P of the detector mode A. Using the profile representation of detector modes, we identify that harvesting is prohibited under certain specific conditions. According to analyses based on moving mirror models, Hawking radiation originates from the Milne modes at past null infinity, that reflect off at the mirror and ultimately transform into real particle modes. Drawing parallels between the Unruh effect and Hawking radiation, our findings indicate an absence of quantum correlations between ``real particles" emitted as Hawking radiation.
The second-order coherence of light is a widely recognized physical quantity used to assess the quantum characteristics of light, and its properties have been extensively investigated in the field of quantum optics. Recently, it has been proposed that second-order coherence can be utilized as an indicator of quantum entanglement. In this study, we evaluated the second-order coherence in the context of the moving-mirror model, which serves as an analog model for Hawking radiation from a black hole. We discuss the relation between entanglement and the second-order coherence of Hawking radiation paying attention to the ``noise'' effect due to the thermality of Hawking radiation, which reduces the quantum correlation in the entanglement-harvesting protocol with two-qubit detectors.
Abstract We investigate the time evolution of reflected entropy and entanglement negativity for mixed state configurations involving two adjacent and disjoint intervals in the radiation flux of moving mirrors by utilizing the AdS/BCFT duality. These measures are computed for the required mixed state configurations by using the respective replica techniques in the large central charge limit of the BCFT1+1. We demonstrate that the results obtained exactly agree with the corresponding holographic computations in the dual bulk AdS3 geometry with an end of the world brane. In this context, the analogues of the Page curves for these measures are obtained for the required configurations in the radiation flux of kink and escaping mirrors which mimic the Hawking radiation from evaporating and eternal black holes respectively.
This article investigates quantum entanglement generated within a one-dimensional cavity where one boundary undergoes prescribed acceleration, a setup designed to mimic aspects of Hawking radiation. We quantify quantum correlations using logarithmic negativity for bipartitions, where subsystem AAA is a given mode and subsystem BBB is the rest of the system. For initial pure states, we also consider a given mode and reconstruct its partner using the Hotta-Sch\"utzhold-Unruh formula, obtaining identical results. Interestingly, this last method offers notable computational efficiency. However, partner modes do not commute, due to the nontrivial multimode entanglement structure. Hence, a pairwise description will not be suitable for describing the full system. Besides, our findings reveal that the expanding cavity effectively acts as a squeezing device, with Hawking-partner pairs largely behaving as two-mode squeezed states. We checked that, in our setting, purification of Hawking modes is predominantly a low-energy process, with high-energetic particles contributing negligibly to the partner modes. Indeed, in both small and large acceleration regimes of the boundaries, quantum entanglement decreases toward the ultraviolet modes, indicating that higher-energy particles are more challenging to entangle and hence less probable to contribute in the purification process. Besides the initial vacuum state, we also consider one-mode squeezed and two-mode squeezed states, in order to confirm if quantum entanglement can be stimulated. Moreover, we analyze its robustness against initial thermal noise. Our analysis is based on numerical simulations and does not assume any approximation beyond the validity of our numerical algorithms. We conclude with a discussion about the possible implementation and observation of our results in the laboratory.
The Hawking effect is an exciting physical prediction lying at the intersection of the two most successful theories of the past century, namely, Einstein’s theory of relativity and quantum mechanics. In this dissertation, we put special emphasis on the quantum aspects of the Hawking process encoded in the entanglement shared by the emitted fluxes of created quanta. In particular, we employ sharp tools from quantum information theory to quantify the entanglement produced by the Hawking effect throughout the black hole evaporation process. Our framework allows us to extend previous calculations of entanglement to a larger set of cases, for instance, the situation where a black hole is immersed in a thermal bath, such as the cosmic microwave background (CMB), and the quantum state of infalling radiation is, therefore, mixed. Motivated by recent intense experimental efforts, we extend our framework to the case of an optical white-black hole pair analog gravity system created by a strong electromagnetic pulse propagating in a non-linear dielectric medium. One of the main results presented in this dissertation is the development of a numerical code that recreates the Hawking process in such an optical analog. Utilizing this code together with our quantum information tools, we study how different input quantum states of light alter the amount of the entanglement produced in the Hawking pairs. We find that although ambient thermal noise and detector inefficiencies, unsurprisingly, tend to reduce quantum correlations in the Hawking process, when horizons are illuminated with single-mode squeezed states of light, the entanglement generated increases in a tunable manner. As a last application in optical analogs, we investigate the laser configuration in which two strong electromagnetic pulses propagate in a non-linear dielectric medium exchanging Hawking quanta, thus, stimulating each other. In such a setup, we observe that not only the number of Hawking quanta created is exponentially increased but also the entanglement shared between the mode of the electromagnetic field inside the laser cavity with the modes of the field outside the cavity grows with time. We conclude that these novel results open a promising window for the observability of the quantum origin of the Hawking effect in the lab.
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.