John Carlos Baez on Nostr: - speaking of relativistic quantum field theory, a fun extra fact is that in quantum ...

- speaking of relativistic quantum field theory, a fun extra fact is that in quantum field theory, the vacuum state maximally violates Bell's inequality. In fact it's even better than that:

"Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system (the "embezzler") via local quantum operations while hardly perturbing the latter. We uncover a deep connection between the operational task of embezzling entanglement and the mathematical classification of von Neumann algebras. Our result implies that relativistic quantum fields are universal embezzlers: Any entangled state of any dimension can be embezzled from them with arbitrary precision. This provides an operational characterization of the infinite amount of entanglement present in the vacuum state of relativistic quantum field theories."

However, none of this is easy to exploit in practice, because the entanglement decays rapidly with the (spacelike) distance.

https://arxiv.org/abs/2401.07292