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Abstract
In quantum measurement theory, a measurement scheme describes how an observable of a given system can be measured indirectly using a probe.
The measurement scheme involves the specification of a probe theory, an initial probe state, a probe observable and a coupling between the system and the probe, so that a measurement of the probe observable after the coupling has ceased reproduces (in expectation) the result of measuring the system observable in the system state. Recent work has shown how local and causal measurement schemes may be described in the context of modelindependent quantum field theory (QFT), but has not addressed the question of whether such measurement schemes exist for all system observables. Here, we present two treatments of this question. The first is a proof of principle which provides a measurement scheme for every local observable
of the quantized real linear scalar field if one relaxes one of the conditions on a QFT measurement scheme by allowing a noncompact coupling region. Secondly, restricting to compact coupling regions, we explicitly construct \emph{asymptotic} measurement schemes for every local observable of the quantized theory. More precisely, we show that for every local system observable $A$ there is an associated collection of measurement schemes for system observables that converge to $A$. All the measurement schemes in this collection have the same fixed compact coupling zone and the same processing region. The convergence of the system observables holds, in particular, in GNS representations of suitable states on the field algebra or the Weyl algebra. In this way, we show that every observable can be asymptotically measured using locally coupled probe theories.
The measurement scheme involves the specification of a probe theory, an initial probe state, a probe observable and a coupling between the system and the probe, so that a measurement of the probe observable after the coupling has ceased reproduces (in expectation) the result of measuring the system observable in the system state. Recent work has shown how local and causal measurement schemes may be described in the context of modelindependent quantum field theory (QFT), but has not addressed the question of whether such measurement schemes exist for all system observables. Here, we present two treatments of this question. The first is a proof of principle which provides a measurement scheme for every local observable
of the quantized real linear scalar field if one relaxes one of the conditions on a QFT measurement scheme by allowing a noncompact coupling region. Secondly, restricting to compact coupling regions, we explicitly construct \emph{asymptotic} measurement schemes for every local observable of the quantized theory. More precisely, we show that for every local system observable $A$ there is an associated collection of measurement schemes for system observables that converge to $A$. All the measurement schemes in this collection have the same fixed compact coupling zone and the same processing region. The convergence of the system observables holds, in particular, in GNS representations of suitable states on the field algebra or the Weyl algebra. In this way, we show that every observable can be asymptotically measured using locally coupled probe theories.
Original language  English 

Number of pages  37 
Journal  Annales Henri Poincare 
DOIs  
Publication status  Published  21 Oct 2022 
Bibliographical note
This is an authorproduced version of the published paper. Uploaded in accordance with the publisher’s selfarchiving policy. Further copying may not be permitted; contact the publisher for details
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