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arXiv:2408.11277 · The European Physical Journal C

Harvesting asymmetric steering via non-identical detectors

Shu-Min Wu, Rui-Di Wang, X. L. Huang, Zejun Wang

Published Jun 27, 2025• 7 citations
arXivHTMLPDF

Abstract

Abstract We investigate asymmetric steering harvesting phenomenon involving two non-identical inertial detectors with different energy gaps, which interact locally with vacuum massless scalar fields. Our study assumes that the energy gap of detector B exceeds that of detector A . It is shown that $$A\rightarrow B$$ A → B steerability is bigger that $$B\rightarrow A$$ B → A steerability, implying that the observer with a small energy gap has more stronger steerability than the other one. We find that the energy gap difference can enlarge the harvesting-achievable range of $$A\rightarrow B$$ A → B steering, while it can also narrow the harvesting-achievable range of $$B\rightarrow A$$ B → A steering at the same time. In addition, the maximal steering asymmetry indicates the transformation between two-way steering and one-way steering in some cases, showing that $$B\rightarrow A$$ B → A steering suffers “sudden death” at the point of this parameter. These results suggest that asymmetric steering exhibits richer and more interesting properties than quantum entanglement harvested from vacuum quantum field.

DOI
10.1140/epjc/s10052-025-14414-4

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Abstract We investigate asymmetric steering harvesting phenomenon involving two non-identical inertial detectors with different energy gaps, which interact locally with vacuum massless scalar fields. Our study assumes that the energy gap of detector B exceeds that of detector A . It is shown that A→BA\rightarrow BA→B A → B steerability is bigger that B→AB\rightarrow AB→A B → A steerability, implying that the observer with a small energy gap has more stronger steerability than the other one. We find that the energy gap difference can enlarge the harvesting-achievable range of A→BA\rightarrow BA→B A → B steering, while it can also narrow the harvesting-achievable range of B→AB\rightarrow AB→A B → A steering at the same time. In addition, the maximal steering asymmetry indicates the transformation between two-way steering and one-way steering in some cases, showing that B→AB\rightarrow AB→A B → A steering suffers “sudden death” at the point of this parameter. These results suggest that asymmetric steering exhibits richer and more interesting properties than quantum entanglement harvested from vacuum quantum field.
Abstract It has been shown that the vacuum state of a free quantum field is entangled and such vacuum entanglement can be harvested by a pair of initially uncorrelated detectors interacting locally with the vacuum field for a finite time. In this paper, we examine the entanglement harvesting phenomenon of two non-identical inertial detectors with different energy gaps locally interacting with massless scalar fields via a Gaussian switching function. We focus on how entanglement harvesting depends on the energy gap difference from two perspectives: the amount of entanglement harvested and the harvesting-achievable separation between the two detectors. In the sense of the amount of entanglement, we find that as long as the inter-detector separation is not too small with respect to the interaction duration parameter, two non-identical detectors could extract more entanglement from the vacuum state than the identical detectors. There exists an optimal value of the energy gap difference when the inter-detector separation is sufficiently large that renders the harvested entanglement to peak. Regarding the harvesting-achievable separation, we further find that the presence of an energy gap difference generally enlarges the harvesting-achievable separation range. Our results suggest that the non-identical detectors may be advantageous to extracting entanglement from vacuum in certain circumstances as compared to identical detectors.
A bstract We investigate the harvesting of quantum steering and its asymmetry between two static detectors locally interacting with a vacuum massless scalar field near an infinite, perfectly reflecting boundary. The detectors are arranged either parallel or orthogonal to the boundary, with detector B assumed to have an energy gap greater than or equal to that of detector A . It is interesting to observe that, with increasing distance between the detectors and the boundary, the boundary tends to suppress quantum steering in one direction while enhancing it in the opposite direction. In the case of identical detectors, steering is symmetric when they are aligned parallel to the boundary. However, orthogonal alignment breaks this symmetry due to their unequal spatial proximity to the boundary. For non-identical detectors in the parallel configuration, the steering from A to B ( A → B ) generally surpasses that from B to A ( B → A ). In contrast, when the detectors are oriented orthogonally to the boundary, the relative strength of A → B and B → A steerability depends on the interplay between the boundary effects and the detectors’ energy gap difference. Across most of the parameter space, the orthogonal alignment tends to enhance B → A steering while suppressing A → B steering compared to the parallel setup. These findings suggest that boundary configurations should be flexibly adjusted according to the directional dependence of steering harvesting in order to optimize quantum information extraction.
We investigate directional quantum steering harvesting by two uniformly accelerated non-identical Unruh-DeWitt detectors coupled to a massless scalar field in the Minkowski vacuum. We show that the Unruh effect does not simply degrade harvested steering, but can reshape its directionality in a strongly parameter-dependent manner. At low detector energy scales, acceleration predominantly suppresses steering, whereas at higher energy scales, moderate acceleration can enhance steering and even activate an initially absent steering direction. Most strikingly, within a finite acceleration window, the Unruh effect enhances steering in one direction while simultaneously suppressing it in the opposite direction, revealing an intrinsically directional influence of relativistic acceleration. Detector non-identicality provides an additional control mechanism: a moderate energy-gap mismatch can enhance or activate one steering direction while suppressing the reverse one, whereas sufficiently large energy-gap mismatch suppresses the harvested steering. Moreover, the maximal steering asymmetry approximately marks the transition from two-way to one-way steering. Our results establish relativistic acceleration and detector non-identicality as means of controlling the strength and directionality of vacuum-harvested quantum correlations.
We investigate the harvesting of quantum steering and its directional asymmetry between two Unruh-DeWitt detectors in a Lorentz-violating BTZ black hole spacetime. Since the detectors are located at different radial positions outside the black hole, they experience inequivalent local environments induced by gravitational redshift, causing Alice to undergo stronger effective thermal noise than Bob. Remarkably, we uncover a counterintuitive phenomenon in which the detector subjected to a higher effective temperature exhibits stronger steerability than the other one, revealing a nontrivial inversion of thermal intuition in curved spacetime. Furthermore, quantum steering survives only within a finite window of detector energy gaps and reaches its maximum within an optimal regime. We find that Lorentz violation suppresses steering most strongly near this optimal energy gap, indicating an enhanced sensitivity of maximal correlation extraction to symmetry breaking effects. Our results demonstrate that Lorentz violation acts as a geometric constraint on the quantum information capacity of spacetime, simultaneously restricting both the strength and the directionality of quantum correlations.
A bstract We study quantum steering and Bell nonlocality harvested by the local interaction of two Unruh-DeWitt detectors with the vacuum massless scalar field, both in the presence of gravitational waves and in Minkowski spacetime. It is shown that quantum steerability under the influence of gravitational waves can be greater than or less than quantum steerability in Minkowski spacetime, which means that the gravitational waves can amplify or degrade the harvested steering. In particular, a resonance effect occurs when the energy gap of the detector is tuned to the frequency of the gravitational wave. We also find that the harvesting-achievable separation range of vacuum steering can be expanded or reduced by the presence of gravitational waves, which depends on the energy gap, the gravitational wave frequency, and the duration of the gravitational wave action. It is interesting to note that two detector systems that satisfy the Bell inequality in most parameter spaces, regardless of the existence of gravitational waves, indicating that steering harvesting cannot be considered to be nonlocal.
Abstract We study, in the framework of the entanglement harvesting protocol, the entanglement harvesting of both a pair of inertial and uniformly accelerated detectors locally interacting with vacuum massless scalar fields subjected to a perfectly reflecting plane boundary. We find that the presence of the boundary generally degrades the harvested entanglement when two detectors are very close to the boundary. However, when the distance between detectors and the boundary becomes comparable to the interaction duration parameter, the amount of the harvested entanglement approaches a peak, which even goes beyond that without a boundary. Remarkably, the parameter space of the detectors’ separation and the magnitude of acceleration that allows entanglement harvesting to occur is enlarged due to the presence of the boundary. In this sense, the boundary plays a double-edged role on entanglement harvesting, degrading in general the harvested entanglement while enlarging the entanglement harvesting-achievable parameter space. A comparison of three different acceleration scenarios of the detectors with respect to the boundary, i.e., parallel, anti-parallel and mutually perpendicular acceleration, shows that the phenomenon of entanglement harvesting crucially depends on the acceleration, the separation between two detectors and the detectors’ distance from the boundary.