Gravitationally Mediated Entanglement of Spin-1/2 Qubits Demonstrates Entanglement Generation Via Dynamical Graviton Exchange

The possibility of entanglement mediated by gravity represents a fundamental question at the intersection of quantum mechanics and general relativity, and recent research explores this phenomenon with a focus on fermionic qubits. Moslem Zarei from Isfahan University of Technology, Mehdi Abdi from Shanghai Jiao Tong University, and Nicola Bartolo and Sabino Matarrese from Universitá di Padova investigate how gravity can create entanglement between distant qubits, using a model where gravitons act as the force carriers. The team demonstrates that entanglement arises from the exchange of these gravitons during forward scattering events, establishing a crucial link between gravitational interactions and quantum correlations. Importantly, their calculations reveal that generating entanglement requires a dynamic gravitational propagator, and that the strength of this entanglement, in certain models, depends on the qubits’ Larmor frequency rather than their mass, offering potential avenues for experimental verification of quantum gravity effects.

Gravitationally mediated entanglement of fermionic qubits: from static to dynamical limits Researchers employ the quantum Boltzmann equation to analyse the gravitationally generated entanglement between two remote qubits, considering two explicit microscopic models. A graviton, the hypothetical particle mediating gravity, serves as the messenger of these interactions, while the qubits exist in a superposition of spatial locations, a configuration that, if entanglement occurs, could provide experimental evidence for the quantum nature of gravity. The team treats the qubits as spin-1/2 particles described by wave packets and establishes that entanglement arises from forward scattering processes involving graviton exchanges. The study demonstrates that entangled states can only be generated when the gravitational interaction is dynamic, not static.

Entanglement from Gravity and Finite Size Effects

This document provides the mathematical foundations for understanding how quantum entanglement can emerge from gravitational interactions between particles, and how the finite size of those particles influences the calculations. Particles are described by wave functions, with the wave packet width indicating the uncertainty in their location. The research employs the quantum Boltzmann equation and focuses on forward scattering. Key approximations include assuming a weak gravitational field and treating particles as having a finite size, which introduces a natural cutoff in the calculations. The document details the derivation of equations describing the evolution of the quantum state, defining the interaction between the particles, and performing mathematical transformations to simplify the calculations.

The integration process results in an expression involving an error function, preventing divergences in the calculations. The authors solve differential equations to determine how the quantum state evolves over time, justifying the approximations made. The document highlights the importance of considering the finite size of particles, as the wave packet width acts as a natural cutoff, ensuring physically meaningful results. The derivations demonstrate how gravitational interactions can lead to quantum entanglement, mixing the quantum states of the particles.

Entanglement from Graviton Scattering, Larmor Frequency Dependence

Scientists investigated the generation of quantum entanglement between two qubits mediated by gravitational interactions, employing the Boltzmann equation to model the process. The research demonstrates that entanglement arises from forward scattering involving graviton exchanges, and crucially, that this effect is only observed in a dynamic regime. Experiments reveal that the amount of entanglement depends on the Larmor frequency of the qubits, rather than their masses, when a magnetic field is applied, particularly for fields exceeding 1 Tesla and particle masses below 10−27 kilograms. The team compared two microscopic models, establishing that for masses exceeding 10−27kg, Model I dominates entanglement generation, while Model II provides a stronger coupling for smaller masses.

Measurements were performed using two parameter sets, one relevant to experiments with atoms, and another suited for elementary particle experiments. Results show appreciable entanglement is established when particle masses are m≳10−23kg in Model I or m≲10−31kg in Model II. The logarithmic negativity, a measure of entanglement, was computed, demonstrating that the entanglement strength transitions from being mass-dependent to being proportional to the product of the Larmor frequencies when a magnetic field is present. These findings suggest potential new avenues for experimental tests of gravitationally induced entanglement, offering an alternative approach to probing quantum aspects of gravity in tabletop experiments.

Gravitational Entanglement via Dynamical Graviton Exchange

This research demonstrates that gravitational interactions can generate quantum entanglement between two qubits, but only under specific conditions. By employing the Boltzmann equation and modeling qubits as spin-1/2 particles interacting via graviton exchange, the team established that entanglement arises from forward scattering processes. Crucially, entanglement generation requires a dynamic limit of the graviton propagator; a static propagator does not induce entanglement. The study further reveals that the amount of entanglement depends on the Larmor frequency of the qubits, rather than their masses, in a model involving a magnetic field.

The researchers derived a specific form for the resulting density matrix, consistent with previous findings regarding entanglement between massive, spinless particles. However, the generated entanglement diminishes as the spatial extent of the qubits’ wave packets increases, indicating a sensitivity to spatial localization. The authors acknowledge that their analysis relies on certain approximations, such as specific limits for the graviton propagator and initial conditions for the qubits. Future work could explore the effects of more complex initial states and investigate the robustness of the generated entanglement to environmental noise. This research contributes to a growing understanding of the interplay between gravity and quantum mechanics, offering insights into how gravitational interactions might influence quantum coherence and potentially enable novel quantum technologies.