Relativistic quantum information measures from unequal-time QFT correlation functions

This paper continues on the program of developing a relativistic quantum information theory in terms of unequal-time correlation functions in quantum field theory (QFT) (Anastopoulos et al., 2023). Here, we focus on the definition of quantum resources from the irreducibly quantum behavior contained in the correlation functions of a QFT. We explain how set-ups with $N$ particle detectors probe the information in the high order field correlation functions. Our main object is the associated hierarchy of probability densities of $N$-detector events. We show that classical probabilistic hierarchies are subject to two conditions: Kolmogorov additivity and measurement independence. QFT violates those conditions, and the degree of violation enables us to define novel quantum resources. We give specific examples in set-ups where the main observables are the times of particle detection events. The new resources capture instances of irreducibly quantum behavior that differs from the quantum behavior encapsulated in Bell inequalities. An interesting byproduct of our analysis is a relativistic state reduction rule for particles detected through scattering.