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Europhysics Letters (EPL)

Schwinger effect of quantum steering for Gaussian states in an electric field

Xiaolong Gong, Ying Zhen Yang, Tonghua Liu

Published Sep 1, 2021• 0 citations
Publisher

Abstract

Abstract In the work, we study the quantum steering for a continuous-variable two-mode squeezed vacuum state shared by Alice and Bob, where Bob's mode experiences a Schwinger effect of a constant electric field. We find that the steering between Alice and Bob decreases with the increasing of the electric field, at the same time the steering between Bob and Anti-Bob is generated. The steering from Alice to Bob results in “sudden death” in the decreasing process, while the steering from Bob to Alice can survive forever. In the production of the steering between Bob and Anti-Bob, the steering from Anti-Bob to Bob shows “sudden birth”, while the steering in the opposite direction is asymptotical. More importantly, we find that the “sudden death” and “sudden birth” appear at the same parameter point, where the steering difference reaches the maximum and the steering transforms between one-way and two-way steering. Moreover, we investigate the case of pulsed electric field, and make a comparison with the case of constant electric field.

DOI
10.1209/0295-5075/ac33cc

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We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a ``sudden death'' and the steering from anti-Bob to Bob experiences a ``sudden birth'' with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed $\mathrm{ln}2$, which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) $s=\mathrm{arccosh}\frac{{\mathrm{cosh}}^{2}r}{1\ensuremath{-}{\mathrm{sinh}}^{2}r}$ is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.

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Abstract Einstein–Podolsky–Rosen (EPR) steering is an important resource for one-sided device-independent quantum information processing. This steering property can be destroyed by the interaction between a quantum system and its environment in practical applications. In this paper, we employ the characteristic function representation of probability distributions to investigate the quantum steering of two-mode continuous-variable states in a laser channel, where both the gain factor and the loss effect are taken into account. Firstly, we analyse the steering time of the two-mode squeezed vacuum state under one-mode and two-mode laser channels, respectively. We find that the gain process introduces additional noise into the two-mode squeezed vacuum state, thereby reducing the steerable time. Secondly, by quantifying EPR steering, we show that two-side loss exhibits smaller steerability than one-side loss, although they share the same two-way steerable time. In addition, we find that the more-gained party can steer the other party’s state, whereas the other party cannot steer the gained party beyond a certain threshold value. In this sense, the gain effect in one party appears to be equivalent to the loss effect in the other party. Our results pave the way for the distillation of EPR steering and quantum information processing in practical quantum channels.

Chinese Physics B•Oct 28, 2025•0 citations
Abstract In the work, we study the quantum steering for a continuous-variable two-mode squeezed vacuum state shared by Alice and Bob, where Bob's mode experiences a Schwinger effect of a constant electric field. We find that the steering between Alice and Bob decreases with the increasing of the electric field, at the same time the steering between Bob and Anti-Bob is generated. The steering from Alice to Bob results in “sudden death” in the decreasing process, while the steering from Bob to Alice can survive forever. In the production of the steering between Bob and Anti-Bob, the steering from Anti-Bob to Bob shows “sudden birth”, while the steering in the opposite direction is asymptotical. More importantly, we find that the “sudden death” and “sudden birth” appear at the same parameter point, where the steering difference reaches the maximum and the steering transforms between one-way and two-way steering. Moreover, we investigate the case of pulsed electric field, and make a comparison with the case of constant electric field.
We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a ``sudden death'' and the steering from anti-Bob to Bob experiences a ``sudden birth'' with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed ln2\mathrm{ln}2ln2, which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) $s=\mathrm{arccosh}\frac{{\mathrm{cosh}}^{2}r}{1\ensuremath{-}{\mathrm{sinh}}^{2}r}$ is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.
The coupled three-mode squeezed vacuum is a representative multimode squeezed Gaussian state featuring unique steerability. This work investigates Gaussian quantum steering distributions of the coupled three-mode squeezed vacuum under an expanding universe. Due to causal separation between the interior and exterior spacetime regions, quantum information behind the event horizon is inaccessible to Alice, Bob and Charlie. We separately analyze steering behaviors for physically accessible and inaccessible modes. Our analysis shows that greater total mean photon number and momentum, combined with reduced expansion volume and expansion rate, enhance quantum steering strength. Notably, Gaussian quantum steering for physically inaccessible modes undergoes the "sudden death" phenomenon when a critical threshold parameter φφφ is exceeded. These results deliver novel insights into quantum correlations in curved spacetime.
Abstract We study the dynamics of Gaussian quantum steering in the background of a Garfinkle–Horowitz–Strominger dilaton black hole. It is found that the gravity induced by dilaton field will destroy the quantum steerability between the inertial observer Alice and the observer Bob who hovers outside the event horizon, while it generates steering-type quantum correlations between the causally disconnected regions. Therefore, the observers can steer each other’s state by local measurements even though they are separated by the event horizon. Unlike quantum entanglement in the dilaton spacetime, the quantum steering experiences catastrophic behaviors such as “sudden death” and “sudden birth” with increasing dilaton charge. In addition, the dilaton gravity destroys the symmetry of Gaussian steering and the latter is always asymmetric in the dilation spacetime. Interestingly, the attainment of maximal steering asymmetry indicates the critical point between one-way and two-way steering for the two-mode Gaussian state in the dilaton spacetime.
We investigate the redistribution and directional properties of Gaussian tripartite quantum steering in de-Sitter space within the continuous-variable framework. By expressing the Bunch-Davies vacuum in terms of the open-chart modes through a Bogoliubov transformation, we derive the covariance matrix of the resulting multipartite Gaussian state and analyze both one-to-two and two-to-one steering configurations. We find that de-Sitter curvature generally suppresses the steering initially shared among the accessible modes, but its influence depends strongly on the steering direction. In particular, while some steering configurations undergo sudden death at finite curvature, two-to-one steering toward a nongravitational mode remains finite throughout the parameter range considered, demonstrating a robustness of tripartite steering absent in its bipartite counterpart. Remarkably, the maximum steering asymmetry occurs at the critical point at which steering in one direction undergoes sudden death, marking the transition from two-way to one-way steering. We further show that the de-Sitter gravitational field can generate tripartite steering involving modes separated by the cosmological horizon. Depending on the steering partition, this curvature-induced steering exhibits persistent one-way or asymmetric two-way behavior, as well as a sudden-birth transition from one-way to two-way steering. These results demonstrate that de-Sitter curvature not only degrades preexisting quantum correlations but also redistributes and generates directional multipartite steering across causally disconnected regions.
Quantum steering is a stronger form of quantum entanglement and is considered to rigorously address the nonlocal correlation in the original Einstein–Podolsky–Rosen paradox. We study the quantum steerability of two classes of continuous-variable (CV) entangled states that are most often employed for CV quantum informatics-entangled coherent states (ECSs) and two-mode-squeezed vacuum (TMSV). We test the two steering criteria by utilizing Heisenberg and entropic uncertainty relations, respectively, and find that the latter can reveal the steerability of ECSs of any size and parity, whereas the former scarcely can. The steering behaviors of the two states are investigated and compared when they experience a noisy environment, i.e., an amplitude damping channel. When the noise is added asymmetrically, e.g., when only one party of the bipartite system is subject to noise, quantum steering can be possible only in one direction, e.g., Alice on Bob’s state but not Bob on Alice’s state. We show the emergence of this one-directional steering for both ECSs and the TMSV in a certain parameter range under decoherence.
Abstract Einstein–Podolsky–Rosen (EPR) steering is an important resource for one-sided device-independent quantum information processing. This steering property can be destroyed by the interaction between a quantum system and its environment in practical applications. In this paper, we employ the characteristic function representation of probability distributions to investigate the quantum steering of two-mode continuous-variable states in a laser channel, where both the gain factor and the loss effect are taken into account. Firstly, we analyse the steering time of the two-mode squeezed vacuum state under one-mode and two-mode laser channels, respectively. We find that the gain process introduces additional noise into the two-mode squeezed vacuum state, thereby reducing the steerable time. Secondly, by quantifying EPR steering, we show that two-side loss exhibits smaller steerability than one-side loss, although they share the same two-way steerable time. In addition, we find that the more-gained party can steer the other party’s state, whereas the other party cannot steer the gained party beyond a certain threshold value. In this sense, the gain effect in one party appears to be equivalent to the loss effect in the other party. Our results pave the way for the distillation of EPR steering and quantum information processing in practical quantum channels.