Recoverability of Gravitational Entanglement under Decoherence

Abstract

Decoherence can make gravitationally generated entanglement arbitrarily small, or even vanishing, without necessarily rendering the effective matter dynamics separable. We ask whether this hidden non-separability can be revealed using strictly local quantum error correction. For Newtonian gravity supplemented by physically relevant localization noise, including environmental noise, and noise from collapse models such as GRW, CSL, and Diósi--Penrose, we analyze when the underlying entangling resource is locally recoverable. For GRW- and CSL-type noise, we analytically establish that strictly local quantum error correction can make the ratio of the effective gravitational interaction strength to the residual decoherence rate arbitrarily large for any parametrization of the collapse model, even in regimes where the unencoded entanglement signal approaches zero. By contrast, the Diósi--Penrose model does not exhibit the same enhancement under bipartite protocol considered here, revealing a qualitative difference. These results show that the loss of detectable entanglement is not equivalent to the loss of a recoverable non-separable resource, and open a route toward practical recovery protocols.