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arXiv · 1806.02407

Relativity of quantum states in entanglement swapping: Violation of Bell's inequality with no entanglement

Chris Nagele·Ebubechukwu O. Ilo-Okeke·Peter P. Rohde·Jonathan P. Dowling·Tim Byrnes
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Abstract

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell violation measurement is performed. From an observer in the laboratory frame, a Bell violation is observed due to entanglement swapping taking place, but in a moving frame the order of the measurements is reversed, and a Bell violation is observed even though no entanglement is present. Although the measurement results are identical, the wavefunctions for the two frames are different--- one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that a maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both the non-local and non-simultaneous feature of entanglement.

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Chris Nagele, Ebubechukwu O. Ilo-Okeke, Peter P. Rohde, Jonathan P. Dowling, Tim Byrnes. 2020-02-17. Relativity of quantum states in entanglement swapping: Violation of Bell's inequality with no entanglement. https://doi.org/10.1016/j.physleta.2020.126301

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