Bell nonlocality from twisted statistics

This paper investigates whether the non-commutative (NC) structure of spacetime, specifically the Moyal plane, can serve as a physical mechanism for generating Bell-nonlocal correlations. While standard local relativistic quantum field theory (QFT) satisfies microcausality, the authors explore how the deformation of multiparticle statistics—induced by the Moyal twist—affects the entanglement of quantum states and their subsequent Bell-test statistics.

Using a free real scalar field on a Moyal-deformed spacetime, the authors utilize the Drinfel’d twist formalism to define the theory. They show that while the one-particle sector and free field dynamics remain identical to the commutative case, the tensor-product structure of the Fock space is modified. By modeling a classical external source that couples locally to the 'dressed' quantum field, they prepare a coherent superposition of momentum-pair configurations. They then analyze the resulting two-qubit state to determine if it violates the CHSH Bell inequality when subjected to local mode measurements.

The researchers find that the twisted multiparticle statistics generate a momentum-dependent phase that acts as a controlled phase between computational wave-packet modes. This phase is invariant under local rephasings and creates entanglement from states that would otherwise be separable in a commutative spacetime. Consequently, the authors prove that for any non-zero deformation, there exists a configuration of local measurements that leads to a violation of the CHSH inequality. The degree of violation is directly linked to the non-commutative parameters and the momentum-space geometry of the prepared wave packets.