Classical theories of gravity produce entanglement

Abstract

The unification of gravity and quantum mechanics remains one of the most profound open questions in science. With recent advances in quantum technology, an experimental idea first proposed by Richard Feynman is now regarded as a promising route to testing this unification for the first time. The experiment involves placing a massive object in a quantum superposition of two locations and letting it gravitationally interact with another mass. In modern versions of the experiment, if the two objects subsequently become entangled, this is considered unambiguous evidence that gravity obeys the laws of quantum mechanics. This conclusion derives from theorems that treat a classical gravitational interaction as a local interaction capable of only transmitting classical, not quantum, information. Here, we argue that the classical gravitational interaction can transmit quantum information, and thus generate entanglement through physically local processes. The effects are found to scale differently to the considered quantum gravity effect, providing information on the form of the experiment required to evidence the quantum nature of gravity.

Figures (6)

• Figure 1: Feynman diagrams for QED or linear quantum gravity. Wiggly blue lines represent photons or gravitons; and black lines represent electrons/positrons or general matter/antimatter particles. For ease of visualization, double lines without arrows represent virtual particles.
• Figure 2: Feynman diagrams for QED with the approximation of classical electromagnetic fields, or linear classical gravity. The wiggly blue lines are classical electromagnetic or gravitational fields/potentials, with the crosses representing classical sources for the fields/potentials. As in Fig. \ref{['fig:Fig1']}, black lines represent electrons/positrons or general matter/antimatter particles; and for ease of visualization, double lines without arrows represent virtual particles.
• Figure 3: Visualization of a version of Feynman's experiment. Two spherical mass distributions (1 and 2) of radius $R$ are placed in quantum superpositions of two locations as N00N states, with blue and red denoting the components separated by $\Delta x$. After gravitationally interacting for a short time, the paths are recombined and entanglement is sought bose2017spinmarletto2017gravitationallyinduced. While Stern-Gerlach interferometry with internal spins is illustrated bose2017spin, alternative setups, such as parallel Mach-Zenhders are also possible marletto2017gravitationallyinduced. Here, $\Delta x$ is depicted larger than the minimum separation $d_{RL}$, but a general configuration can be implemented, including $\Delta x \ll d_{RL}$.
• Figure 4: a) Feynman diagram corresponding to Wick contraction \ref{['eq:WickCrissCross']}. The $1i$ and $2j$ label the first and second objects, with $i,j \in \{L,R\}$. b) The corresponding diagram when there is a classical gravity interaction (the two circles with crosses indicate the two classical sources of gravity, i.e. the two matter objects). The amplitudes of both diagrams are found to be vanishing. In contrast to standard perturbative QFT diagrams, the external legs here represent position-like states rather than definite momentum states, as detailed in the main text, with the arrows indicating time evolution.
• Figure 5: First and second order Feynman diagrams that contribute towards the relative quantum phases $\Delta \varphi_1$ and $\Delta \varphi_2$ in \ref{['eq:PsiRelativeClassicalPhase']} but not entanglement. The $1i$ and $2j$ label the first and second matter distributions, with $i,j \in \{L,R\}$. The two circles with crosses indicate the two classical sources of gravity, i.e. the two matter distributions. As stated also in Fig. \ref{['fig:CrissCross']}, in contrast to standard perturbative QFT diagrams, the external legs represent position-like states, with the arrows indicating time evolution.