Entanglement in Markovian hybrid classical-quantum theories of gravity

Markovian master equations underlie many areas of modern physics and, despite their apparent simplicity, they encode a rich and complex dynamics which is still under active research. We identify a class of continuous variable Markovian master equations for which positivity and complete positivity become equivalent. We apply this result to characterize the positivity of the partially transposed evolution of bipartite Gaussian systems, which encodes the dynamics of entanglement. Finally, the entangling properties of models of classical gravity interacting with quantum matter are investigated in the context of the experimental proposals to detect gravitationally induced entanglement. We prove that entanglement generation can indeed take place within these models. We prove that entanglement generation can indeed take place within these models. In particular, by focusing on the Diósi-Penrose model for two gravitationally interacting masses, we show that entanglement-based experiments have the potential to either falsify the model entirely or constrain the free parameter of the model $R_0$ up to values six orders of magnitude above the current state of the art.

💡 Research Summary

The paper investigates whether hybrid models in which a classical gravitational field interacts with quantum matter can generate entanglement, a question of central importance for recent proposals to detect gravitationally‑induced entanglement (GIE) as a signature of quantum gravity. The authors focus on continuous‑variable (CV) Gaussian Markovian master equations of the Gorini‑Kossakowski‑Sudarshan‑Lindblad (GKSL) type, where the Hamiltonian is quadratic in the canonical operators and the Lindblad operators are linear.

First, they prove a mathematically non‑trivial result: for a class of Kossakowski matrices of the form
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