Gravitationally-induced Conversion of Local Coherence to Entanglement

TL;DR

This paper analyzes whether gravity can generate quantum entanglement by examining a two-mass setup through the lens of quantum resource theory. It shows that the gravitational interaction acts as a unitary, coherence-preserving channel that redirects local coherence into bipartite entanglement, accompanied by exact complementarity relations between coherence and entanglement. The results establish that initial coherence is a necessary resource for entanglement and quantifies how its magnitude bounds the maximum achievable entanglement, with maximal entanglement requiring maximal initial coherence. This resource-theoretic perspective offers a refined interpretive framework for upcoming experiments and provides concrete criteria for designing setups to witness gravity-induced entanglement.

Abstract

In recent years, the quantum nature of gravity has attracted significant attention as one of the most important problems in modern physics. Here, we analyze the mechanism of gravitationally-induced entanglement from the perspective of quantum resource theory. Building on the framework of Bose et al. [Phys. Rev. Lett. 119, 240401 (2017)], we show that the gravitational interaction acts as a unitary channel, redistributing quantum resources between two spatially superposed masses. Specifically, we demonstrate that the resulting bipartite entanglement originates from the coherent conversion of local quantum coherence -- initially present in each subsystem -- into shared non-local correlations. We derive exact, analytical complementarity relations quantifying this conversion, link the decay of local coherence directly to the growth of entanglement, and support these findings with numerical simulations. Our results clarify the underlying mechanism and establish gravity as a coherence-to-entanglement conversion channel, offering a refined interpretive basis for forthcoming experimental tests. Crucially, we show that initial coherence is a necessary condition for entanglement generation and that its degree bounds the maximum achievable entanglement, with maximal entanglement requiring initial maximal coherence.

Figures (7)

• Figure 1: Two test masses are maintained adjacent to each other in a superposition of spatially localized states $|L\rangle$ and $|R\rangle$.
• Figure 2: The $l_1$-norm of coherence $C_{l_{1}}(\rho_{A})$ plotted as a function of the phases $\Delta \phi_{L R}$ and $\Delta \phi_{R L}$.
• Figure 3: The negativity $\mathcal{N}(\rho_{AB})$ plotted as a function of the phases $\Delta \phi_{L R}$ and $\Delta \phi_{R L}$.
• Figure 4: The squared $l_1$-norm of coherence and squared negativity as functions of the total accumulated phase $\Delta \phi_{L R}+\Delta \phi_{R L}$. The blue solid line represents $C_{l_{1}}^{2}(\rho_{A})$, the red dashed curve represents $\mathcal{N}^{2}(\rho_{AB})$, and the black dot-dashed curve represents their sum $C_{l_{1}}(\rho_{A})^{2}+\mathcal{N} (\rho_{AB})^{2}$.
• Figure 5: The relative entropy of coherence and the von Neumann entropy of the reduced state of the subsystem $A$ as functions of the total accumulated phase $\Delta \phi_{L R}+\Delta \phi_{R L}$. The blue solid line represents $C_{r}(\rho_{A})$, the red dashed curve represents $\mathcal{E}(\rho_{AB})$, and the black dot-dashed curve represents their sum $C_{r}(\rho_{A})+\mathcal{E}(\rho_{AB})$.