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arXiv:2205.01967 · Physical review. D/Physical review. D.

Complementarity-entanglement tradeoff in quantum gravity

Yusef Maleki, Alireza Maleki

Published Apr 28, 2022• 9 citations
arXivHTMLPDF

Abstract

The quantization of gravity remains one of the most important---yet extremely elusive---challenges at the heart of modern physics. Any attempt to resolve this long-standing problem seems to be doomed, as the route to any direct empirical evidence (i.e., detecting gravitons) that sheds light on the quantum aspect of gravity is far beyond the current capabilities. Recently, it was discovered that gravitationally induced entanglement, tailored in the interferometric frameworks, can be used to witness the quantum nature of gravity. Even though these schemes offer promising tools for investigating quantum gravity, many fundamental and empirical aspects of the schemes are yet to be discovered. Considering the fact that, besides quantum entanglement, the quantum uncertainty and complementarity principles are the two other foundational aspects of quantum physics, the quantum nature of gravity needs to manifest all of these features. Here, we lay out an interferometric platform for testing these nonclassical aspects of quantum mechanics in the quantum gravity setting, which connects gravity and quantum physics in a broader and deeper context. As we show in this work, all of these fundamental features of quantum gravity can be framed and thoroughly analyzed in an interferometric scheme.

DOI
10.1103/physrevd.105.086024

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The quantization of gravity remains one of the most important---yet extremely elusive---challenges at the heart of modern physics. Any attempt to resolve this long-standing problem seems to be doomed, as the route to any direct empirical evidence (i.e., detecting gravitons) that sheds light on the quantum aspect of gravity is far beyond the current capabilities. Recently, it was discovered that gravitationally induced entanglement, tailored in the interferometric frameworks, can be used to witness the quantum nature of gravity. Even though these schemes offer promising tools for investigating quantum gravity, many fundamental and empirical aspects of the schemes are yet to be discovered. Considering the fact that, besides quantum entanglement, the quantum uncertainty and complementarity principles are the two other foundational aspects of quantum physics, the quantum nature of gravity needs to manifest all of these features. Here, we lay out an interferometric platform for testing these nonclassical aspects of quantum mechanics in the quantum gravity setting, which connects gravity and quantum physics in a broader and deeper context. As we show in this work, all of these fundamental features of quantum gravity can be framed and thoroughly analyzed in an interferometric scheme.
The quest for a quantum theory of gravity remains a central challenge in modern physics, driven by the goal of unifying general relativity and quantum mechanics. Direct experimental access to quantum gravitational effects is notoriously difficult due to the inaccessibility of the Planck scale. Recent proposals, however, suggest that gravitationally induced quantum entanglement between two massive particles, realized through advanced quantum interferometric techniques, could provide empirical evidence for the quantum nature of gravity. We demonstrate that the geometrical configuration of an interferometer plays a decisive role in entanglement generation. Our analysis reveals that geometric optimization can substantially enhance the gravitationally induced phase shift, thereby improving the prospects for experimental detection of gravity-mediated entanglement. Moreover, we show that standard approximations employed in prior proposals may severely limit predictive accuracy and compromise experimental feasibility.
Abstract The effect of gravity is a key factor in understanding the physical phenomenon. Quantizing gravity is challenging task due to weak interactions of gravity in quantum world. The quantum nature of gravity can be witnessed by entanglement in an interferometric platform [Phys. Rev. D 105, 086024 (2022)]. A natural question arises concerning whether the quantization of gravity can be observed via other means. In this work, we propose an effective approach to witnessing the gravity-induced quantumness by quantum uncertainty relations, including entropy-based and coherence-based uncertainty relations. The theoretical frameworks for wave-particle, entropic uncertainty and coherence are established, which can prove the quantum nature of gravity. The three-measurement entropic uncertainty and coherence exhibit the oscillatory features for the gravity-induced phases in the interferometric scheme. It is found that the evolutionary dynamics of coherence is inversely correlated with the measured uncertainty. It can be interpreted that the reduction of systemic quantum resource leads to the increase of entropic uncertainty, and vice versa. When the entropic uncertainty reaches zero, systemic coherence is the maximum value, providing a viable physical explanation for the gravity-induced quantumness. It shows that the entropic uncertainty and coherence can be regarded as the reliable indicators for capturing the gravity-induced quantumness. Compared to entanglement-based gravity quantization scheme, it shows that the capabilities are equivalent for detecting the gravity-induced quantumness using entropy uncertainty, coherence, and entanglement. The results could lay a solid theoretical foundation for the potential applications of quantum gravity in quantum information science.
Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.
The pursuit of a quantum theory of gravity, aiming to unify general relativity and quantum mechanics, remains one of the most enduring challenges in physics. Because of the extreme energy scales associated with the Planck regime, direct experimental evidence for quantum gravity remains elusive. However, recent proposals suggest that quantum entanglement between two massive particles may provide a pathway to probe the quantum nature of gravity. In this study, we examine the interferometer geometries proposed in these works, with particular attention to the commonly used approximation that neglects phase contributions from the vertical segments of the particle trajectories. Our analysis shows that this approximation can lead to incorrect predictions and, in certain parameter regimes, to null results where entanglement would otherwise be expected. We derive exact solutions that incorporate the full particle trajectories and demonstrate that the vertical arms can significantly affect the accumulated phase. Crucially, we identify configurations in which the induced entanglement vanishes entirely, a feature missed by simplified treatments. These findings show that accounting for the full interferometer geometry is not merely a refinement, but is essential for accurately assessing gravity-induced entanglement.
The quantum nature of gravity is one of physics' greatest unsolved problems, with existing experimental proposals facing formidable challenges in maintaining spatial superpositions of massive objects against decoherence. We propose a fundamentally different approach that bypasses these difficulties. The central insight is that a quantum gravitational field can imprint a gauge-invariant phase on a particle's wavefunction even along an open trajectory, arising from the quantum backreaction of the source. This phase, which manifests prior to the final recombination stage of an interferometer and cannot be generated by a classical gravitational field, provides an operationally direct witness to the quantumness of gravity. Our experimental design uses a single photon whose accumulated gravitational phase due to the Earth is transferred via absorption to auxiliary atoms near the end of the interferometer sequence, preserving the open-path character essential for the test. We scale the interferometer to yield a detectable phase of order 10−310^{-3}10−3 rad and show how non-local correlation measurements on the atoms can access this gauge-invariant signature. Leveraging established quantum optical and atomic techniques, this proposal offers a feasible path to distinguish quantum from classical gravity. A positive result would provide the first experimental evidence for the quantum nature of gravitational fields, with profound implications for quantum gravity theories.
The aim of this article is to provide an introduction to the use of quantum information methods for investigating the interface between quantum theory and gravity. To this end, we discuss the basic principles of two current research streams that use this approach. The first one explores a phenomenon known as gravitationally induced entanglement, which aims to infer whether the gravitational field responsible for the interaction between two massive bodies must be quantized or not. The second stream investigates causal structures, thereby providing indirect evidence that spacetime may exhibit non-classical behavior. Before presenting these topics, we briefly review some fundamental concepts and experiments from quantum information theory, such as the Mach-Zehnder interferometer, the Stern-Gerlach experiment, Bell inequalities and entanglement, and the language of quantum circuits.