Real-space Bell inequalities in de Sitter

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.

22 pages without appendices (31 pages in total), 10 figures. Comments and references added. Matches version published in JCAP

References in corpus (12)

• Non-Gaussianity as a signature of a quantum theory of gravity
• Signals of a Quantum Universe
• Bell violation in the Sky
• Quantum Entanglement in Time
• Discord and Decoherence
• Infinite violation of Bell inequalities in inflation
• The Quantum Information of Cosmological Correlations
• Real-space entanglement in the Cosmic Microwave Background
• Four-mode squeezed states: two-field quantum systems and the symplectic group $\mathrm{Sp}(4,\mathbb{R})$
• Bipartite temporal Bell inequalities for two-mode squeezed states
• Real-space entanglement of quantum fields
• Long-range enhanced mutual information from inflation

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• Universal role of curvature in vacuum entanglement
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• Imprints of screened dark energy on nonlocal quantum correlations
• A Flat Space Analogue for the Quantum Origin of Structure
• Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum
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