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arXiv:2405.07141 · Journal of Cosmology and Astroparticle Physics

Cosmological Bell tests with decoherence effects

Chon Man Sou, Junqi Wang, Yi Wang

Published Oct 1, 2024• 10 citations
arXivHTMLPDF

Abstract

Abstract The inflationary universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Operators involving the momenta of the fluctuations can be rewritten into pseudo-spin operators, such as the Gour-Khanna-Mann-Revzen (GKMR) pseudo-spin. Making use of these pseudo-spin operators, cosmological Bell inequalities can be formulated. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. In this work, we focus on primordial curvature perturbations. Since curvature perturbations arise from gravity, their action includes the Gibbons-Hawking-York boundary term. We clarify the role of the boundary term in selecting suitable initial conditions for linear perturbations. After that, we proceed to the interactions of cosmological perturbations, including the bulk and boundary interaction terms, which introduce decoherence effects. These decoherence effects change the expectation value of the Bell operator, and gradually restore the Bell inequality. We describe this process by a “Bell test curve”, which offers a window around 5 e-folds for testing the quantum origin of cosmological perturbations. We also explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test curve.

DOI
10.1088/1475-7516/2024/10/084

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Abstract The inflationary universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Operators involving the momenta of the fluctuations can be rewritten into pseudo-spin operators, such as the Gour-Khanna-Mann-Revzen (GKMR) pseudo-spin. Making use of these pseudo-spin operators, cosmological Bell inequalities can be formulated. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. In this work, we focus on primordial curvature perturbations. Since curvature perturbations arise from gravity, their action includes the Gibbons-Hawking-York boundary term. We clarify the role of the boundary term in selecting suitable initial conditions for linear perturbations. After that, we proceed to the interactions of cosmological perturbations, including the bulk and boundary interaction terms, which introduce decoherence effects. These decoherence effects change the expectation value of the Bell operator, and gradually restore the Bell inequality. We describe this process by a “Bell test curve”, which offers a window around 5 e-folds for testing the quantum origin of cosmological perturbations. We also explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test curve.
The primordial fluctuations during inflation are widely believed to seed the Large Scale Structure of the universe. However, it remains unknown whether these fluctuations have a quantum nature. According to the inflation theory, the expanding universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Therefore, cosmological Bell inequalities are well motivated and can be formulated using pseudo-spin operators, constructed from operators involving the momenta of the fluctuations. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. However, the cosmological Bell test faces several obstructions, including decoherence and the fast-decaying momenta. We thus study the Bell test on scalar modes and tensor modes with decoherence from the interactions of cosmological perturbations, including the bulk and boundary interaction terms. We explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test. We also discuss the possibility of constructing Bell tests for the entanglement between polarizations, which may avoid the fast-decaying momenta problem and be another way, besides the tabletop experiments and large gravitational waves detectors, to test the quantum nature of gravity.
Inflationary cosmology successfully accounts for the observed properties of primordial fluctuations using quantum field theory in an expanding background. However, the quantum nature of these fluctuations has not been experimentally established, since classical stochastic models could reproduce the observed two-point statistics by construction. Existing approaches to testing primordial quantumness focus primarily on Bell inequalities, which provide a sharp conceptual criterion but are difficult to implement with cosmological observables. In this work we adopt a falsification-based approach. We define a precise classical hypothesis for the origin of primordial perturbations (local stochastic fields admitting a positive probability distribution) and identify inequality constraints that must be satisfied within this class. We show how violations of these classicality inequalities can be probed using realistic cosmological observables, without invoking Bell tests or non-commuting measurement settings. We further identify symmetry-protected spectator sectors in which quantum coherence is parametrically preserved during inflation, allowing violations of observable magnitude to survive decoherence. Our results show that large-scale structure and future 21 cm surveys provide a viable and quantitative route to falsifying classical stochastic descriptions of primordial fluctuations.
One of the cornerstones of inflationary cosmology is that primordial density fluctuations have a quantum mechanical origin. However, most physicists consider that such quantum mechanical effects disappear in CMB data due to decoherence. In this conference report, we show that the violation of Bell inequalities in an initial state of our universe increases exponentially with the number of modes to measure in inflation. This indicates that some evidence that our universe has a quantum mechanical origin may survive in CMB data, even if quantum entanglement decays exponentially afterward due to decoherence.
Abstract Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as cosmological density fluctuations. In this work, we show how Bell operators can be constructed for quantum fields in real space, and for Gaussian states we compute their expectation value in terms of the field power spectra. We then apply our formalism to a scalar field in de-Sitter space-time. We find that, in spite of the tremendous production of entangled particles with opposite wave momenta on large scales, Bell inequalities are not violated in real space. The reason is that, when considering measurements of a field at two distinct locations in real space, one implicitly traces over the configuration of the field at every other location, leading to a mixed bipartite system. This “effective decoherence” effect is responsible for the erasure of quantum features, and casts some doubts on our ability to reveal the quantum origin of cosmological structures. We finally discuss these results in the light of quantum discord.
We investigate the role of the bipartite temporal Bell inequality, an analogue of the spatial Bell inequality, in probing the quantum imprints of primordial perturbations when the initially chosen Bunch-Davies vacuum is replaced by a coherent state. Although it is based on the same principles of locality and realism, its primary advantage lies in the fact that it does not require two distinct set of observable for its construction. Instead, measurements performed on a single component of the pseudo-spin operator at different times are sufficient. Consequently, it is particularly well suited for cosmological scenarios, where observational constraints typically allow access to only one component of the pseudo-spin operator. Assuming a coherent state as the initial condition, we derive an analytical expression for the expectation value of the bipartite temporal Bell operator and demonstrate the absence of temporal Bell violation in such a scenario. Interestingly, the results for squeezed coherent state is found to differ - albeit slightly - from those of squeezed vacuum state for large values of the squeezing parameter. This suggests that the ability to distinguish among different initial states of primordial perturbations does not rely on the violation of temporal Bell inequality. Furthermore, the dependence of the temporal Bell inequality on a purely imaginary phase factor of the wave function appears to be an unique feature, which is entirely absent in the context of spatial Bell inequalities.
In spite of the macroscopic character of the primordial fluctuations, the standard inflationary distribution (that obtained using linear mode equations) exhibits inherently quantum properties, that is, properties which cannot be mimicked by any stochastic distribution. This is demonstrated by a Gedanken experiment for which certain Bell inequalities are violated. These violations are in principle measurable because, unlike for Hawking radiation from black holes, in inflationary cosmology we can have access to both members of correlated pairs of modes delivered in the same state. We then compute the effect of decoherence and show that the violations persist provided the decoherence level (and thus the entropy) lies below a certain nonvanishing threshold. Moreover, there exists a higher threshold above which no violation of any Bell inequality can occur. In this regime, the distributions are ``separable'' and can be interpreted as stochastic ensembles of fluctuations. Unfortunately, the precision which is required to have access to the quantum properties is so high that, in practice, an observational verification seems excluded.