Gravitationally-induced Conversion of Local Coherence to Entanglement

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.

💡 Research Summary

In this paper the authors revisit the proposal by Bose et al. (Phys. Rev. Lett. 119, 240401 (2017)) that two spatially superposed massive particles can become entangled solely through their mutual gravitational interaction. Using the formalism of quantum resource theory, they treat the gravitational interaction as a unitary channel that preserves the total amount of quantum coherence while redistributing it between the two subsystems. Each mass is modeled as a two‑level “orbital qubit” with basis states |L⟩ and |R⟩. Initially both masses are prepared in the equal superposition (|L⟩+|R⟩)/√2, which is a maximally coherent product state. The gravitational interaction introduces configuration‑dependent phases ϕ_{ij} that can be written as Δϕ_{LR} and Δϕ_{RL}. The evolution operator U_G = Σ_{i,j} e^{iϕ_{ij}}|ij⟩⟨ij| is diagonal in the computational basis, i.e., an incoherent unitary operation in the language of coherence resource theory. Consequently the global coherence C(ρ_AB) remains constant, but the reduced coherence of each particle, C(ρ_A) and C(ρ_B), can decrease, with the lost coherence appearing as bipartite entanglement.

The authors quantify coherence with two standard measures – the l₁‑norm and the relative entropy of coherence – and quantify entanglement with negativity (or equivalently concurrence) and the von Neumann entropy of the reduced state (entanglement entropy). For the symmetric initial state they derive exact complementarity relations: C_{l₁}²(ρ_A) + N²(ρ_AB) = 1, C_{l₁}²(ρ_A) + C²(ρ_AB) = 1, C_r(ρ_A) + E(ρ_AB) = 1. These equalities show that any increase in entanglement is accompanied by an exactly corresponding decrease in local coherence, confirming that gravity acts as a perfect coherence‑to‑entanglement converter.

To explore the role of the initial resource, the analysis is extended to a general pure product state |ψ(0)⟩ = (√p_A|L⟩ + √{1‑p_A}|R⟩)_A ⊗ (√p_B|L⟩ + √{1‑p_B}|R⟩)_B, with arbitrary occupation probabilities p_A, p_B ∈