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arXiv:2606.29144

Gaussian quantum steering of coupled three-mode squeezed vacuum in an expanding universe

Guang-Wei Mi, Xiaofen Huang, Tinggui Zhang

quant-phSubmitted Jun 28, 2026• Announced Jun 30, 2026• 0 citations
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Abstract

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 $φ$ is exceeded. These results deliver novel insights into quantum correlations in curved spacetime.

Comments
11 pages, 8 figures

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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.
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.
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.
Multipartite Einstein-Podolsky-Rosen (EPR) steering and multimode quantum squeezing are essential resources for various quantum applications. The paper focuses on studying a coupled three-mode squeezed vacuum (C3MSV), which is a typical multimode squeezed Gaussian state and will exhibit peculiar steering property. Using the technique of integration within ordered products, we give the normal-ordering form for the coupled three-mode squeezing operator and derive the general analytical expressions of the statistical quantities for the C3MSV. Under Gaussian measurements, we analyze all bipartite Gaussian steerings (including no steering, one-way steering, and two-way steering) in detail and study the monogamy relations for the C3MSV. Then, we study the decoherence of all these steerings in noisy channels and find that sudden death will happen in a certain threshold time. Through the steerings shared in the C3MSV, we propose conceptual (and ideal) schemes of remotely generating Wigner negativity by performing appropriate photon subtraction(s) in the local position. Our obtained results may lay a solid theoretical foundation for a future practical study. We also believe that the C3MSV will be one of good candidate resources in future quantum protocols.
We systematically investigate the directional dependence of Gaussian quadripartite quantum steering and its redistribution among different modes in the background of a Schwarzschild black hole. For physically accessible sectors, we identify three distinct behaviors: (i) steering from non-gravitational to gravitational observers undergoes sudden death at maximal asymmetry with the Hawking temperature, marking the crossover from two-way to one-way steerability; (ii) steering in the opposite direction decays monotonically and vanishes only in the extreme black hole limit, highlighting its directional sensitivity to spacetime curvature; (iii) steering from hybrid gravitational-non-gravitational partitions to non-gravitational mode persists at a finite asymptotic value set by the initial squeezing parameter. Moreover, all inaccessible steerings generated by the Hawking effect exhibit an intrinsic asymmetry, with their specific behavior being strongly dependent on the steering direction.
Abstract Realistic quantum systems are affected by the expanding universe in their preparation and quantum information processing. In this paper, we study the relationship between the Gaussian quantum steering distribution and the parameters of the expanding universe. The expansion process of the universe can be described as a channel acting on a two-mode squeezed Gaussian state, with the evolution of quantum steering from the asymptotic past to the asymptotic future resulting in new distributions parameterized by cosmic parameters. We find that Gaussian quantum steering is more sensitive to the volume change of the expanding universe than the expansion rate, and the Gaussian quantum steering generated by particles with suitable mass and small momentum is more affected by the expanding universe.
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.