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Abstract
The process of quantum measurement is considered in the algebraic framework of quantum field theory on curved spacetimes. Measurements are carried out on one quantum field theory, the "system", using another, the "probe". The measurement process involves a dynamical coupling of "system" and "probe" within a bounded spacetime region. The resulting "coupled theory" determines
a scattering map on the uncoupled combination of the "system" and "probe" by reference to natural "in" and "out" spacetime regions. No specific interaction is assumed and all constructions are local and covariant.
Given any initial state of the probe in the "in" region, the scattering map
determines a completely positive map from "probe" observables in the "out" region to "induced system observables", thus providing a measurement scheme for the latter. It is shown that the induced system observables may be localized in the causal hull
of the interaction coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory.
Postselected states conditioned on measurement outcomes are obtained using DaviesLewis instruments that depend on the initial probe state. Composite measurements involving causally ordered coupling regions are also considered. Provided that the scattering map obeys a causal factorization property, the causally ordered composition of the individual instruments coincides with the composite instrument;
in particular, the instruments may be combined in either order if the coupling regions are causally disjoint. This is the central consistency property of the proposed framework.
The general concepts and results are illustrated by an example in which both "system" and "probe" are quantized linear scalar fields, coupled by a quadratic interaction term with compact spacetime support. System observables induced by simple probe observables are calculated exactly, for sufficiently weak coupling, and compared with first order perturbation theory.
a scattering map on the uncoupled combination of the "system" and "probe" by reference to natural "in" and "out" spacetime regions. No specific interaction is assumed and all constructions are local and covariant.
Given any initial state of the probe in the "in" region, the scattering map
determines a completely positive map from "probe" observables in the "out" region to "induced system observables", thus providing a measurement scheme for the latter. It is shown that the induced system observables may be localized in the causal hull
of the interaction coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory.
Postselected states conditioned on measurement outcomes are obtained using DaviesLewis instruments that depend on the initial probe state. Composite measurements involving causally ordered coupling regions are also considered. Provided that the scattering map obeys a causal factorization property, the causally ordered composition of the individual instruments coincides with the composite instrument;
in particular, the instruments may be combined in either order if the coupling regions are causally disjoint. This is the central consistency property of the proposed framework.
The general concepts and results are illustrated by an example in which both "system" and "probe" are quantized linear scalar fields, coupled by a quadratic interaction term with compact spacetime support. System observables induced by simple probe observables are calculated exactly, for sufficiently weak coupling, and compared with first order perturbation theory.
Original language  English 

Pages (fromto)  851–889 
Number of pages  39 
Journal  Communications in Mathematical Physics 
Volume  378 
Issue number  2 
Early online date  27 Jul 2020 
DOIs  
Publication status  Published  Sept 2020 
Bibliographical note
© The Author(s) 2020Profiles

Measurement in quantum field theory: what’s the problem, and what’s the cure?
Chris Fewster (Chair)
24 Jul 2023 → 27 Jul 2023Activity: Talk or presentation › Invited talk

Measurement in quantum field theory: what’s the problem, and what’s the cure?
Chris Fewster (Keynote/plenary speaker)
13 Mar 2023Activity: Talk or presentation › Invited talk

Institute for Quantum Optics and Quantum Information (IQOQI) Vienna
Chris Fewster (Visitor)
13 Mar 2023 → 14 Mar 2023Activity: Visiting an external institution › Academic