Bell inequalities violation within non-Bunch-Davies states

TL;DR

This paper investigates how non-Bunch-Davies states in de Sitter space can generate quantum nonlocality, violate Bell inequalities, and have implications for quantum information, depending on the vacuum choice and temperature effects.

Contribution

It demonstrates that non-Bunch-Davies vacua can produce Bell inequality violations and quantum correlations that persist under decoherence, revealing their potential for quantum information applications.

Findings

Quantum nonlocality can be generated via Markovian evolution.

Bell inequality violation depends on vacuum choice and temperature.

Non-Bunch-Davies vacua can surpass measurement uncertainty bounds.

Abstract

We study the quantum nature of non-Bunch-Davies states in de Sitter space by evaluating CHSH inequality on a localized two-atom system. We show that quantum nonlocality can be generated through the Markovian evolution of two-atom, witnessed by a violation of CHSH inequality on its final equilibrium state. We find that the upper bound of inequality violation is determined by different choices of de Sitter-invariant vacua sectors. In particular, with growing Gibbons-Hawking temperature, the CHSH bound degrades monotonously for Bunch-Davies vacuum sector. Due to the intrinsic correlation of non-Bunch-Davies vacua, we find that the related violation of inequality can however drastically increase after certain turning point, and may persist for arbitrarily large environment decoherence. This implies that the CHSH inequality is useful to classify the initial quantum state of the Universe. Finally, we clarify that the witnessed intrinsic correlation of non-Bunch-Davies vacua can be utilized for quantum information applications, e.g., surpassing the Heisenberg uncertainty bound of quantum measurement in de Sitter space.