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arXiv:1703.04325

Why we need to quantise everything, including gravity

Chiara Marletto, Vlatko Vedral

Published Mar 13, 2017• 2 citations
arXivHTMLPDF

Abstract

There is a long-standing debate about whether gravity should be quantised. A powerful line of argument in favour of quantum gravity considers models of hybrid systems consisting of coupled quantum-classical sectors. The conclusion is that such models are inconsistent: either the quantum sector's defining properties necessarily spread to the classical sector, or they are violated. These arguments have a long history, starting with the debates about the quantum nature of the electromagnetic fields in the early days of quantum theory. Yet, they have limited scope because they rely on particular dynamical models obeying restrictive conditions, such as unitarity. In this paper we propose a radically new, more general argument, relying on less restrictive assumptions. The key feature is an information-theoretic characterisation of both sectors, including their interaction, via constraints on copying operations. These operations are necessary for the existence of observables in any physical theory, because they constitute the most general representation of measurement interactions. Remarkably, our argument is formulated without resorting to particular dynamical models, thus being applicable to any hybrid system, even those ruled by "post-quantum" theories. Its conclusion is also compatible with partially quantum systems, such as those that exhibit features like complementarity, but may lack others, such as entanglement. As an example, we consider a hybrid system of qubits and rebits. Surprisingly, despite the rebit's lack of complex amplitudes, the signature quantum protocols such as teleportation are still possible.

DOI
10.48550/arxiv.1703.04325

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There is a long-standing debate about whether gravity should be quantised. A powerful line of argument in favour of quantum gravity considers models of hybrid systems consisting of coupled quantum-classical sectors. The conclusion is that such models are inconsistent: either the quantum sector's defining properties necessarily spread to the classical sector, or they are violated. These arguments have a long history, starting with the debates about the quantum nature of the electromagnetic fields in the early days of quantum theory. Yet, they have limited scope because they rely on particular dynamical models obeying restrictive conditions, such as unitarity. In this paper we propose a radically new, more general argument, relying on less restrictive assumptions. The key feature is an information-theoretic characterisation of both sectors, including their interaction, via constraints on copying operations. These operations are necessary for the existence of observables in any physical theory, because they constitute the most general representation of measurement interactions. Remarkably, our argument is formulated without resorting to particular dynamical models, thus being applicable to any hybrid system, even those ruled by "post-quantum" theories. Its conclusion is also compatible with partially quantum systems, such as those that exhibit features like complementarity, but may lack others, such as entanglement. As an example, we consider a hybrid system of qubits and rebits. Surprisingly, despite the rebit's lack of complex amplitudes, the signature quantum protocols such as teleportation are still possible.
Abstract There is a long-standing debate about whether gravity should be quantised. A powerful line of argument in favour of quantum gravity considers models of hybrid systems consisting of coupled quantum–classical sectors. The conclusion is that such models are inconsistent: either the quantum sector’s defining properties necessarily spread to the classical sector, or they are violated. These arguments have a long history, starting with the debates about the quantum nature of the electromagnetic fields in the early days of quantum theory. Yet, they have limited scope because they rely on particular dynamical models obeying restrictive conditions, such as unitarity. In this paper we propose a radically different, more general argument, relying on less restrictive assumptions. The key feature is an information-theoretic characterisation of both sectors, including their interaction, via constraints on copying operations. These operations are necessary for the existence of observables in any physical theory, because they constitute the most general representation of measurement interactions. Remarkably, our argument is formulated without resorting to particular dynamical models, thus being applicable to any hybrid system, even those ruled by “post-quantum” theories. Its conclusion is also compatible with partially quantum systems, such as those that exhibit features like complementarity, but may lack others, such as entanglement. As an example, we consider a hybrid system of qubits and rebits. Surprisingly, despite the rebit’s lack of complex amplitudes, the signature quantum protocols such as teleportation are still possible.
Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.
We argue for the universality of quantum theory using a dynamical consistency argument, within a specific Hamiltonian setting. We analyse two different types of coupling between simple quantum harmonic oscillators. Each illustrates an aspect of the free and interacting quantum fields and shows the inadequacy of semiclassical models. In particular, we establish that requiring the canonical algebra to be preserved under joint unitary dynamics rules out specific hybrid classical-quantum models. We apply our reasoning to the gravitational field in the linear regime, coupled to the quantised electromagnetic field and, separately, to quantised matter. We conclude with a comparison to DeWitt's analysis of quantum measurement, in which the apparatus, if classical, must be at least stochastic to preserve the Heisenberg Uncertainty Principle. We also note that stochastic models are inconsistent with the strict version of conservation principles, even if they comply with a probabilistic (on average) conservation.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
It is a matter of ongoing discussion whether quantum states can become entangled while only interacting via a classical mediator. This lively debate is deeply interwoven with the question of whether entanglement studies can prove the quantum nature of gravity. However, the answer to this fundamental question depends crucially on which hybrid quantum-classical theory is used. In this Letter, we demonstrate that entanglement by a classical mediator is possible within the framework of hybrid van Hove theory, showing that existing no-go theorems on that matter do not universally apply to hybrid theories in general. After briefly recapitulating the key features of the hybrid van Hove theory, we show this using the example of two quantum spins coupled by a classical harmonic oscillator. By deriving the spin density matrix for this scenario and comparing it to its equivalent for a pure quantum system, we show that entanglement between the two spins is generated in both cases. Conclusively, this is illustrated by presenting the purity and concurrence of the spin-spin system as a decisive measure for entanglement. Our results further imply that quantum entanglement studies cannot rule out consistent quantum theories featuring classical gravity.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.