Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Entanglement of quantum systems via a classical mediator in hybrid van Hove theory

Sebastian Ulbricht, Andrés Darío Bermúdez Manjarres, Marcel Reginatto

TL;DR

The paper shows that entanglement between quantum systems can be mediated by a classical subsystem within Hybrid van Hove (HvH) theory, challenging universal no-go theorems. By analyzing a two-qubit system coupled through a classical or quantum harmonic oscillator, the authors derive reduced spin density matrices that share the same Bloch–Fano structure, with entanglement quantified via purity and concurrence. For weak coupling, the entanglement dynamics in the HvH hybrid case closely match the fully quantum case, implying that classical mediators do not necessarily prohibit quantum correlations and that conclusions about classical gravity based on entanglement tests must be carefully contextualized. The End Matter further clarifies the HvH framework, including the decomposition of classical densities into trajectories and the treatment of classical phase, and demonstrates a concrete correspondence between quantum and classical-quantum hybrid descriptions, especially when the classical distribution width matches the quantum Wigner function. Overall, the work shows that entanglement via classical mediation is feasible in HvH theory and cautions against overgeneralizing no-go results in the search for a consistent quantum-classical description of gravity.

Abstract

It is a matter of ongoing discussion whether quantum states can become entangled while only interacting via a classical mediator. This lively debate is deeply interwoven with the question of whether entanglement studies can prove the quantum nature of gravity. However, the answer to this fundamental question depends crucially on which hybrid quantum-classical theory is used. In this letter, we demonstrate that entanglement by a classical mediator is possible within the framework of hybrid van Hove theory, showing that existing no-go theorems on that matter do not universally apply to hybrid theories in general. After briefly recapitulating the key features of the hybrid van Hove theory, we show this using the example of two quantum spins coupled by a classical harmonic oscillator. By deriving the spin density matrix for this scenario and comparing it to its equivalent for a pure quantum system, we show that entanglement between the two spins is generated in both cases. Conclusively, this is illustrated by presenting the purity and concurrence of the spin-spin system as a decisive measure for entanglement. Our results further imply that quantum entanglement studies cannot rule out consistent quantum theories featuring classical gravity.

Entanglement of quantum systems via a classical mediator in hybrid van Hove theory

TL;DR

The paper shows that entanglement between quantum systems can be mediated by a classical subsystem within Hybrid van Hove (HvH) theory, challenging universal no-go theorems. By analyzing a two-qubit system coupled through a classical or quantum harmonic oscillator, the authors derive reduced spin density matrices that share the same Bloch–Fano structure, with entanglement quantified via purity and concurrence. For weak coupling, the entanglement dynamics in the HvH hybrid case closely match the fully quantum case, implying that classical mediators do not necessarily prohibit quantum correlations and that conclusions about classical gravity based on entanglement tests must be carefully contextualized. The End Matter further clarifies the HvH framework, including the decomposition of classical densities into trajectories and the treatment of classical phase, and demonstrates a concrete correspondence between quantum and classical-quantum hybrid descriptions, especially when the classical distribution width matches the quantum Wigner function. Overall, the work shows that entanglement via classical mediation is feasible in HvH theory and cautions against overgeneralizing no-go results in the search for a consistent quantum-classical description of gravity.

Abstract

It is a matter of ongoing discussion whether quantum states can become entangled while only interacting via a classical mediator. This lively debate is deeply interwoven with the question of whether entanglement studies can prove the quantum nature of gravity. However, the answer to this fundamental question depends crucially on which hybrid quantum-classical theory is used. In this letter, we demonstrate that entanglement by a classical mediator is possible within the framework of hybrid van Hove theory, showing that existing no-go theorems on that matter do not universally apply to hybrid theories in general. After briefly recapitulating the key features of the hybrid van Hove theory, we show this using the example of two quantum spins coupled by a classical harmonic oscillator. By deriving the spin density matrix for this scenario and comparing it to its equivalent for a pure quantum system, we show that entanglement between the two spins is generated in both cases. Conclusively, this is illustrated by presenting the purity and concurrence of the spin-spin system as a decisive measure for entanglement. Our results further imply that quantum entanglement studies cannot rule out consistent quantum theories featuring classical gravity.
Paper Structure (13 sections, 35 equations, 2 figures)

This paper contains 13 sections, 35 equations, 2 figures.

Table of Contents

  1. Introduction---
  2. Hybrid van Hove theory---
  3. Two spins coupled by a harmonic oscillator---
  4. Quantum case---
  5. Hybrid case---
  6. Measures of entanglement---
  7. Summary and Discussion---
  8. Acknowledgments---
  9. End Matter
  10. The classical probability densities as a decomposition of trajectories---
  11. Requirements for the phase of the classical wave function---
  12. On classical wavefunctions for single trajectories---
  13. Coherent state for the quantum oscillator and its classical analogue---

Figures (2)

  • Figure 1: In HvH theory, two quantum spins can become entangled while only interacting indirectly via a classical oscillator as the mediator.
  • Figure 2: Comparison of the purity $\mathcal{P}(\rho)$ and the concurrence $\mathcal{C}(\rho)$ in the quantum case (dashed) and hybrid case (solid) with $\Sigma=\sqrt{\hbar/m\omega}$, respectively. Both measures are plotted for the interaction strength of $g^2/m \omega^3 \hbar=1$ (green), $g^2/m \omega^3 \hbar=1/2$ (red), and $g^2/m \omega^3 \hbar=1/4$ (blue). We find that the measures of entanglement for both quantum and hybrid systems closely resemble each other, especially when the interactions are weak ($g^2\ll m \omega^3\hbar$).