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arXiv:0809.1907 · Physical Review A

Quantum connectivity of space-time and gravitationally induced decorrelation of entanglement

Timothy C. Ralph, Gerard J Milburn, T. G. Downes

Published Feb 26, 2009• 69 citations
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Abstract

We discuss an alternative formulation of the problem of quantum optical fields in a curved space-time using localized operators. We contrast this formulation with the standard approach and find observable differences for entangled states. We propose an experiment in which an entangled pair of optical pulses are propagated through nonuniform gravitational fields and find that the alternative formulation predicts decorrelation of the optical entanglement under experimentally realistic conditions.

DOI
10.1103/physreva.79.022121

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We discuss an alternative formulation of the problem of quantum optical fields in a curved space-time using localized operators. We contrast this formulation with the standard approach and find observable differences for entangled states. We propose an experiment in which an entangled pair of optical pulses are propagated through nonuniform gravitational fields and find that the alternative formulation predicts decorrelation of the optical entanglement under experimentally realistic conditions.
Abstract Experiments witnessing the entanglement between two particles interacting only via the gravitational field have been proposed as a test whether gravity must be quantized. In the language of quantum information, a non-quantum gravitational force would be modeled by local operations with classical communication (LOCC), which cannot generate entanglement in an initially unentangled state. This idea is criticized as too constraining on possible alternatives to quantum gravity. We present a parametrized model for the gravitational interaction of quantum matter on a classical spacetime, inspired by the de Broglie–Bohm formulation of quantum mechanics, which results in entanglement and thereby provides an explicit counterexample to the claim that only a quantized gravitational field possesses this capability.
Quantum Physics Quantum mechanics and the general theory of relativity represent two pillars of modern physics, but unification of the two theories remains an open problem. Theories of quantum gravity abound, but they tend to lack an experimental foundation. One such proposed theory, event formalism, predicts that a pair of entangled particles decorrelate as they pass through different regions of the gravitational well of a planetary object. Xu et al. present results of a quantum optical test of this proposal using the quantum satellite Micius. Using entangled photon pairs, one sent to the satellite and the other retained on Earth, they find no evidence for the predicted decorrelation effects. The results may help shed light on the interplay between quantum theory and gravity. Science , this issue p. [132][1] [1]: /lookup/doi/10.1126/science.aay5820
Abstract No experiment to date has provided evidence for quantum features of the gravitational interaction. Recently proposed tests suggest looking for the generation of quantum entanglement between massive objects as a possible route towards the observation of such features. Motivated by advances in optical cooling of mirrors, here we provide a systematic study of entanglement between two masses that are coupled gravitationally. We first consider the masses trapped at all times in harmonic potentials (optomechanics) and then the masses released from the traps. This leads to the estimate of the experimental parameters required for the observation of gravitationally induced entanglement. The optomechanical setup demands LIGO-like mirrors and squeezing or long coherence times, but the released masses can be light and accumulate detectable entanglement in a timescale shorter than their coherence times. No macroscopic quantum superposition develops during the evolution. We discuss the implications from such thought experiments regarding the nature of the gravitational coupling.
Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum correlations, such as entanglement, may exhibit different behavior to purely classical correlations in curved space. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph et al [ 5 ] and Ralph and Pienaar [ 1 ], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's Space QUEST (Space—Quantum Entanglement Space Test) mission, and study the feasibility of the mission scheme.