Einstein-Podolsky-Rosen Steering in Three Coupled Harmonic Oscillators

• URL: http://arxiv.org/abs/2601.01307v1
• Date: Sun, 04 Jan 2026 00:08:14 GMT
• Title: Einstein-Podolsky-Rosen Steering in Three Coupled Harmonic Oscillators
• Authors: Ayoub Ghaba, Radouan Hab Arrih, Elhoussine Atmani, Abdallah Slaoui,
• Abstract summary: Quantum steering is essential for understanding correlations in multi-body systems.<n>We derive analytical expressions for quantum steering in all possible directions using the Wigner function framework.<n>Our results indicate that excitations significantly enhance quantum steering across the system.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Quantum steering is one of the most intriguing phenomena in quantum mechanics and is essential for understanding correlations in multi-body systems. Despite its importance, analytical results for coupled three-body oscillators remain scarce. In this work, we investigate this phenomenon through a geometrical diagonalization approach, which reduces the degrees of freedom associated with the system's steering properties. Specifically, we derive analytical expressions for quantum steering in all possible directions using the Wigner function framework, as it provides a complete description of the system's quantum state. Our results indicate that excitations significantly enhance quantum steering across the system; this stands in contrast to the ground state $(0,0,0)$, which exhibits no steerable correlations. Furthermore, both the directionality and topology of these correlations are governed by the spatial distribution of the excitations rather than their magnitude. We also observe symmetric steering behavior between oscillators $x$, $y$, and $z$ under equivalent excitation conditions, which can be formalized as $S^{(n,m,l)}_{x\to z}(θ)=S^{(n,m,l)}_{x\to y}(-θ),\quad S^{(n,m,l)}_{z\to x}(θ)=S^{(n,m,l)}_{y\to x}(-θ)$, and $S^{(n,m,l)}_{y\to z}(θ)=S^{(n,m,l)}_{z\to y}(-θ)$. Therefore, we elucidate how excitation levels and mixing angles generate and enhance steering in three coupled harmonic oscillators.

Related papers

• Assessing the entanglement of three coupled harmonic oscillators [0.0]
  Quantum entanglement serves as a key phenomenon in understanding correlations in many-body systems.<n>In this work, we introduce a geometrical diagonalization approach that constrains angles, thereby reducing the degrees of freedom in the entanglement analysis.
  arXiv  Detail & Related papers  (2026-01-03T21:35:46Z)
• Exact Relation Between Wehrl-Rényi Entropy and Many-Body Entanglement [13.703543201381892]
  We establish an exact relation between the Wehrl-R'enyi entropy (WRE) $S_W(2)$, which is the 2nd R'enyi entropy of the Husimi function of the entire system.<n>We analytically derive the WRE for several representative many-body states, including Haar-random states, the Greenberger-Horne-Zeilinger (GHZ) state, and the W state.
  arXiv  Detail & Related papers  (2025-09-19T14:43:58Z)
• Unifying Floquet theory of longitudinal and dispersive readout [33.7054351451505]
  We devise a Floquet theory of longitudinal and dispersive readout in circuit QED.<n>We apply them to superconducting and spin-hybrid cQED systems.
  arXiv  Detail & Related papers  (2024-07-03T18:00:47Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Gaussian quantum steering in a nondegenerate three-level laser [0.0]
  Steering is a type of nonseparable quantum correlation, where its inherent asymmetric feature makes it distinct from Bell-nonlocality and entanglement. In this paper, we investigate quantum steering in a two-mode Gaussian state $% hatvarrho_c_1c_2$ coupled to a two-mode vacuum reservoir.
  arXiv  Detail & Related papers  (2023-12-08T10:17:05Z)
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors [46.76612530830571]
  We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (detectors'') We explore the dynamics of density and of entanglement entropy in the chain, for various values of $rho_a$ and $M$.
  arXiv  Detail & Related papers  (2023-11-21T21:41:11Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• On parametric resonance in the laser action [91.3755431537592]
  We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser. We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
  arXiv  Detail & Related papers  (2022-08-22T09:43:57Z)
• Understanding the propagation of excitations in quantum spin chains with different kind of interactions [68.8204255655161]
  It is shown that the inhomogeneous chains are able to transfer excitations with near perfect fidelity. It is shown that both designed chains have in common a partially ordered spectrum and well localized eigenvectors.
  arXiv  Detail & Related papers  (2021-12-31T15:09:48Z)
• Dynamics of Non-Gaussian Entanglement of Two Magnetically Coupled Modes [0.0]
  This paper surveys the quantum entanglement of two coupled harmonic oscillators via angular momentum. We study the effect of the anisotropy $ R=omega_12/omega_22 $, $omega_c$, asymmetry $ |n-m| $ and dynamics on the entanglement.
  arXiv  Detail & Related papers  (2021-08-09T15:52:34Z)
• Dynamics and Redistribution of Entanglement and Coherence in Three Time-Dependent Coupled Harmonic Oscillators [0.0]
  We resolve the Schr"odinger equation by using time-dependent rotation together with a linear quench model. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes.
  arXiv  Detail & Related papers  (2020-07-29T11:19:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.