This paper points out the importance of the assumption of locality of physical interactions, and the concomitant necessity of propagation of an entity (in this case, off-shell quanta—virtual gravitons) between two nonrelativistic test masses in unveiling the quantum nature of linearized gravity through a laboratory experiment. At the outset, we will argue that observing the quantum nature of a system is not limited to evidencing $O\left(\hslash \right)$ corrections to a classical theory: it instead hinges upon verifying tasks that a classical system cannot accomplish. We explain the background concepts needed from quantum field theory and quantum information theory to fully appreciate the previously proposed table-top experiments, namely forces arising through the exchange of virtual (off-shell) quanta, as well as local operations and classical communication (LOCC) and entanglement witnesses. We clarify the key assumption inherent in our evidencing experiment, namely the locality of physical interactions, which is a generic feature of interacting systems of quantum fields around us, and naturally incorporate microcausality in the description of our experiment. We also present the types of states the matter field must inhabit, putting the experiment on firm relativistic quantum-field-theoretic grounds. At the end, we use a nonlocal theory of gravity to illustrate how our mechanism may still be used to detect the qualitatively quantum nature of a force when the scale of nonlocality is finite. We find that the scale of nonlocality, including the entanglement entropy production in local and nonlocal gravity, may be revealed from the results of our experiment.

A recently proposed experimental protocol for quantum gravity induced entanglement of masses (QGEM) requires in principle realizable, but still very ambitious, set of parameters in matter-wave interferometry. Motivated by easing the experimental realization, in this paper, we consider the parameter space allowed by a slightly modified experimental design, which mitigates the Casimir potential between two spherical neutral test masses by separating the two macroscopic interferometers by a thin conducting plate. Although this setup will reintroduce a Casimir potential between the conducting plate and the masses, there are several advantages of this design. First, the quantum gravity induced entanglement between the two superposed masses will have no Casimir background. Secondly, the matter-wave interferometry itself will be greatly facilitated by allowing both the mass ${10}^{-16}–{10}^{-15}\mathrm{kg}$ and the superposition size $\mathrm{\Delta }x\sim 20\mu \mathrm{m}$ to be a one-two order of magnitude smaller than those proposed earlier, and thereby also two orders of magnitude smaller magnetic field gradient of ${10}^4{\mathrm{Tm}}^{-1}$ to create that superposition through the Stern-Gerlach effect. In this context, we will further investigate the collisional decoherences and decoherence due to vibrational modes of the conducting plate.

Recently, a theoretical and an experimental protocol known as quantum-gravity-induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses, each placed in a superposition of two locations. If after eliminating all nongravitational interactions between them the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e., graviton. In this paper we explore extensions of the QGEM experiment to multidimensional quantum objects and examine a range of different experiment geometries, in order to determine which would generate entanglement faster. We conclude that when a sufficiently high decoherence rate is introduced, multicomponent superpositions can outperform the two-qubit setup. With low decoherence however, and given a maximum distance $\mathrm{\Delta }x$ between any two spatial states of a superposition, a set of two qubits placed in spatial superposition parallel to one another will outperform all other models given realistic experimental parameters. This is further verified with an experiment simulation, showing that $O\left({10}^3\right)$ measurements are required to reject the no-entanglement hypothesis with a parallel-qubit setup without decoherence at a $99.9\%$ confidence level. The number of measurements increases when decoherence is introduced. When the decoherence rate reaches 0.125 Hz, six-dimensional qudits are required as the two-qubit system entanglement cannot be witnessed anymore. However, in this case, $O\left({10}^6\right)$ measurements will be required. One can group the witness operators to measure in order to reduce the number of measurements (up to tenfold). However, this may be challenging to implement experimentally.

Probing quantum mechanics and quantum aspects of general relativity, along with the sensing and constraining of classical gravity, can all be enabled by unprecedented spatial sizes of superpositions of massive objects. In this paper, we show that there is a feasible setup sourced by realizable magnetic field gradients $O\left(10\text{–}100\right)\mathrm{T}$ ${\mathrm{m}}^{-1}$ to construct a large spatial superposition of $O\left({10}^{-4}\text{–}{10}^{-8}\right)\mathrm{m}$ for $O\left({10}^{-17}\text{–}{10}^{-14}\right)\mathrm{kg}$ masses within a time of up to 0.1–10 seconds. The scale of superpositions is unrestricted as long as quantum coherence can be maintained for a required amount of time.

Recently, a protocol called quantum-gravity-induced entanglement of masses (QGEM) that aims to test the quantum nature of gravity using the entanglement of two qubits was proposed. The entanglement can arise only if the force between the two spatially superposed masses is occurring via the exchange of a mediating virtual graviton. In this paper we examine a possible improvement of the QGEM setup by introducing a third mass with an embedded qubit so that there are now three qubits to witness the gravitationally generated entanglement. We compare the entanglement generation for different experimental setups with two and three qubits and find that a three-qubit setup where the superpositions are parallel to each other leads to the highest rate of entanglement generation within $\tau =5\mathrm{s}$. We show that the three-qubit setup is more resilient to the higher rate of decoherence. The entanglement can be detected experimentally for the two-qubit setup if the decoherence rate $\gamma$ is $\gamma <0.11\mathrm{Hz}$ compared to $\gamma <0.16\mathrm{Hz}$ for the three-qubit setup. However, the introduction of an extra qubit means that more measurements are required to characterize entanglement in an experiment. We conduct experimental simulations and estimate that the three-qubit setup would allow detecting the entanglement in the QGEM protocol at a $99.9\%$ certainty with $O\left({10}^4\right)–O\left({10}^5\right)$ measurements when $\gamma \in [0.1,0.15]\mathrm{Hz}$. Furthermore, we find that the number of needed measurements can be reduced to $O\left({10}^3\right)–O\left({10}^5\right)$ if the measurement schedule is optimized using joint Pauli basis measurements. For $\gamma >0.06\mathrm{Hz}$ the three-qubit setup is favorable compared to the two-qubit setup in terms of the minimum number of measurements needed to characterize the entanglement. Thus, the proposed setup here provides a promising avenue for implementing the QGEM experiment.

A large spatial quantum superposition of size $O\left(1\text{–}10\right)\mu \text{m}$ for mass $m\sim {10}^{-17}\text{–}{10}^{-14}$ kg is required to probe the foundations of quantum mechanics and test the classical and quantum nature of gravity via entanglement in a laboratory. In this paper, we will show that it is possible to accelerate the two spin states of a macroscopic nanocrystal sourced by the inhomogeneous nonlinear magnetic field in a Stern-Gerlach-type setup. We will assume that the electronic spin can be embedded at the center of the nanocrystal, such as the nitrogen-vacancy (NV) center of diamond. Our analysis will be generic to any dopant or any material. We will show that we can create a desired superposition size within $1\text{–}2$ s by catapulting the trajectories of the two spin states with a modest magnetic field gradient and then recombine the trajectories for a coherent interference. We will show the demanding nature of the precision required in the magnetic field to recover a $99\%$ spin coherence confidence level at the moment of interference.