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arXiv:2405.07362

Entanglement Dynamics in Quantum Continuous-Variable States

Ankit Kumar

Published May 12, 2024• 0 citations
arXivHTMLPDF

Abstract

Due to the weakness of gravitational coupling, all quantum experiments up to date in which gravity plays a role utilized the field of the Earth. Since this field undergoes practically undetectable back-action from quantum particles, it effectively admits a classical description as a fixed background Newtonian field or spacetime. This argument strongly motivates theoretical and experimental research towards a demonstration of gravitation between two quantum masses, as this is one of the most straightforward scenarios where quantum features of gravity could be observed. Several proposals studied the possibility of generating entanglement between two massive objects. Along the same lines, with a particular focus on gravity, this thesis introduces general tools to tackle interaction-mediated entanglement and applies them to two particles prepared in continuous-variable states.

DOI
10.48550/arxiv.2405.07362

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Due to the weakness of gravitational coupling, all quantum experiments up to date in which gravity plays a role utilized the field of the Earth. Since this field undergoes practically undetectable back-action from quantum particles, it effectively admits a classical description as a fixed background Newtonian field or spacetime. This argument strongly motivates theoretical and experimental research towards a demonstration of gravitation between two quantum masses, as this is one of the most straightforward scenarios where quantum features of gravity could be observed. Several proposals studied the possibility of generating entanglement between two massive objects. Along the same lines, with a particular focus on gravity, this thesis introduces general tools to tackle interaction-mediated entanglement and applies them to two particles prepared in continuous-variable states.
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Gravity-induced entanglement has been proposed as a method for testing the non-classical nature of gravity via tabletop experiments. While most existing proposals are restricted to the Newtonian limit, the frame dragging effect offers access to genuinely post-Newtonian features of the gravitational interaction and remains comparatively less explored. Here, we study gravity-induced entanglement generated by frame dragging in an interferometric setting and compute the entanglement phase between the rotational degrees of freedom of a source mass and the paths of a particle in two complementary ways: (i) via Schrödinger evolution with a quantized Lense-Thirring Hamiltonian in the large angular momentum limit, and (ii) via the on-shell action of linearized quantum gravity within the stationary phase approximation. Both approaches yield the same entanglement phase, consistent with the proper time difference between the interferometer arms. The path integral derivation further reveals how gravitational retardation modifies the entanglement phase, thereby making the local, relativistically causal linearized-gravity description explicit. Under the standard locality/mediator assumptions used in existing arguments, the resulting entanglement would witness non-classicality of the gravitational interaction.
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We study the continuous variable entanglement of a system of two particles under the influence of Earth's gravitational field. We determine a phase-space description of this bipartite system by calculating its Wigner function and verify its entanglement by applying a generalization of the PPT criterion for non-Gaussian states. We also examine the influence of gravity on an idealized entanglement protocol to be shared between stations at different potentials based on the correlation of states of the gravitational quantum well.