Relativistic Quantum Information from Unequal-Time QFT Correlation Functions

TL;DR

This paper develops a relativistic quantum information framework using unequal-time QFT correlation functions, identifying quantum resources through violations of classical probability conditions and exploring implications for particle detection and state reduction.

Contribution

It introduces a novel approach to quantify quantum resources in QFT via hierarchy of detector correlations, highlighting violations of classical probability conditions.

Findings

QFT correlation functions violate Kolmogorov additivity and measurement independence.

New quantum resources are defined based on the degree of violation.

Relativistic state reduction rules are derived for scattering detections.

Abstract

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)[arXiv:2208.03696]. 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 differ 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.