Detector-based measurements for QFT: two issues and an AQFT proposal

Abstract

We present and investigate two issues within the measurement scheme for QFT presented by J. Polo-Gómez, L. J. Garay and E. Martín-Martínez in "A detector-based measurement theory for quantum field theory". We point out some discrepancies that arise when the measurement scheme is applied to contextual field states and show that $n$-point function assignments based on local processing regions sometimes lead to inconsistencies. To solve these issues, we modify the measurement scheme to use non-relativistic detectors to induce an update rule for algebraic states in the Haag-Kastler formulation of quantum field theory. In this way, $n$-point functions can be consistently evaluated across any region having a definite causal relation with measurements.

arXiv comment16 pages, 4 figures; v1 includes major revisions

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• Quantum entanglement in cosmology
• Einstein causality of quantum measurements in the Tomonaga-Schwinger picture