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arXiv:2310.06596 · Physical review. D/Physical review. D.

Detector-based measurements for QFT: Two issues and an algebraic QFT proposal

Nicola Pranzini, Esko Keski-Vakkuri

Published Feb 18, 2025• 2 citations
arXivHTMLPDF

Abstract

We present and investigate two issues within the measurement scheme for QFT presented by Polo-G\'omez et al. [Phys. Rev. D 105, 065003 (2022)]. 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 nonrelativistic 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.

DOI
10.1103/physrevd.111.045016

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Abstract Despite quantum theory’s remarkable success at predicting the statistical results of experiments, many philosophers worry that it nonetheless lacks some crucial connection between theory and experiment. Such worries constitute the Quantum Measurement Problems. One can broadly identify two kinds of worries: (1) pragmatic: it is unclear how to model our measurement processes in order to extract experimental predictions, and (2) realist: we lack a satisfying metaphysical account of measurement processes. While both issues deserve attention, the pragmatic worries have worse consequences if left unanswered: If our pragmatic theory-to-experiment linkage is unsatisfactory, then quantum theory is at risk of losing both its evidential support and its physical salience. Avoiding these risks is at the core of what I will call thePragmatic Measurement Problem. Fortunately, the pragmatic measurement problem is not too difficult to solve. For non-relativistic quantum theory, the story goes roughly as follows: One can model each of quantum theory’s key experimental successes on a case-by-case basis by using a measurement chain. In modeling this measurement chain, it is pragmatically necessary to switch from using a quantum model to a classical model at some point. That is, it is pragmatically necessary to invoke a Heisenberg cut at some point along the measurement chain. Past this case-by-case measurement framework, one can then strive for a wide-scoping measurement theory capable of modeling all (or nearly all) possible measurement processes. For non-relativistic quantum theory, this leads us to our usual projective measurement theory. As a bonus, proceeding this way also gives us an empirically meaningful characterization of the theory’s observables as (positive) self-adjoint operators. But how does this story have to change when we move into the context of quantum field theory (QFT)? It is well known that in QFT almost all localized projective measurements violate causality, allowing for faster-than-light signaling; These are Sorkin’s impossible measurements. Thus, the story of measurement in QFT cannot end as it did before with a projective measurement theory. But does this then mean that we need to radically rethink the way we model measurement processes in QFT? Are our current experimental practices somehow misguided? Fortunately not. I will argue that (once properly understood) our old approach to modeling quantum measurements is still applicable in QFT contexts. We ought to first use measurement chains to build up a case-by-case measurement framework for QFT. Modeling these measurement chains will require us to invoke what I will call a QFT-cut. That is, at some point along the measurement chain we must switch from using a QFT model to a non-QFT model. Past this case-by-case measurement framework, we can then strive for both a new wide-scoping measurement theory for QFT and an empirically meaningful characterization of its observables. It is at this point that significantly more theoretical work is needed. This paper ends by briefly reviewing the state of the art in the physics literature regarding the modeling of measurement processes involving quantum fields.

arXiv:2205.09608•Synthese•Sep 20, 2023•15 citations
We present and investigate two issues within the measurement scheme for QFT presented by Polo-G'omez et al. [Phys. Rev. D 105, 065003 (2022)]. We point out some discrepancies that arise when the measurement scheme is applied to contextual field states and show that nnn-point function assignments based on local processing regions sometimes lead to inconsistencies. To solve these issues, we modify the measurement scheme to use nonrelativistic detectors to induce an update rule for algebraic states in the Haag-Kastler formulation of quantum field theory. In this way, nnn-point functions can be consistently evaluated across any region having a definite causal relation with measurements.
We propose a measurement theory for quantum fields based on measurements made with localized nonrelativistic systems that couple covariantly to quantum fields (like the Unruh-DeWitt detector). Concretely, we analyze the positive operator-valued measure induced on the field when an idealized measurement is carried out on the detector after it coupled to the field. Using an information-theoretic approach, we provide a relativistic analogue to the quantum-mechanical L\"uders update rule to update the field state following the measurement on the detector. We argue that this proposal has all the desirable characteristics of a proper measurement theory. In particular it does not suffer from the ``impossible measurements'' problem pointed out by Rafael Sorkin in the 1990s which shows that idealized measurements cannot be used in quantum field theory.
Abstract Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293–305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. https://doi.org/10.1103/PhysRevD.104.025012 ) establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. Sorkin [1] labels such scenarios ‘impossible measurements’. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the ‘impossible measurements’ problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez et al. (Phys Rev D, 2022. https://doi.org/10.1103/physrevd.105.065003 ) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851–889, 2020). Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating ‘impossible measurements’, the abandonment of the operational interpretation of local algebras A(O){\mathcal {A}}(O)A(O) A ( O ) as representing possible operations carried out in region O , and the interpretation of state update rules. Finally, we examine the form that the ‘impossible measurements’ problem takes in histories-based approaches and we discuss the remaining challenges.
In relativistic Quantum Field Theory (QFT) ideal measurements of certain observables are physically impossible without violating causality. This prompts two questions: i) can a given observable be ideally measured in QFT, and ii) if not, in what sense can it be measured? Here we formulate a necessary and sufficient condition that any measurement, and more generally any state update (quantum operation), must satisfy to respect causality. Our focus is scalar QFT, although our results should be applicable to observables in fermionic QFT. We argue that for unitary `kicks' and operations involving 1-parameter families of Kraus operators, e.g. Gaussian measurements, the only causal observables are smeared fields and the identity - the basic observables in QFT. We provide examples with more complicated operators such as products of smeared fields, and show that the associated state updates are acausal, and hence impossible. Despite this, one can still recover expectation values of such operators, and we show how to do this using only causal measurements of smeared fields.
These lectures present a brief introduction to measurement theory for QFT in possibly curved spacetimes introduced by the author and R. Verch [Comm. Math. Phys. 378 (2020) 851-889]. Topics include: a brief introduction to algebraic QFT, measurement schemes in QFT, state updates, multiple measurements and the resolution of Sorkin's "impossible measurement" problem. Examples using suitable theories based on Green hyperbolic operators are given, and the interpretational significance of the framework is briefly considered. The basic style is to give details relating to QFT while taking for granted various facts from the theory of globally hyperbolic spacetimes.
The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the wavefunction'' with relativity of simultaneity, and the difficulty of maintaining causality in the rules for measurement highlighted by ``impossible measurement'' scenarios. Thereafter, the issue is considered from the perspective of mathematical physics. To this end, quantum field theory is described in a model-independent, operator algebraic setting, on generic Lorentzian spacetime manifolds. The process of measurement is modelled by a localized dynamical coupling between a quantum field called the ``system'', and another quantum field, called the ``probe''. The result of the dynamical coupling is a scattering map, whereby measurements carried out on the probe can be interpreted as measurements of induced observables on the system. The localization of the dynamical coupling allows it to derive causal relations for the induced observables. It will be discussed how this approach leads to the concept of selective or non-selective system state updates conditioned on the result of probe measurements, which in turn allows it to obtain conditional probabilities for consecutive probe measurements consistent with relativistic causality and general covariance, without the need for a physical collapse of the wavefunction. In particular, the problem of impossible measurements is resolved. Finally, there is a brief discussion of accelerated detectors and other related work.
Abstract Despite quantum theory’s remarkable success at predicting the statistical results of experiments, many philosophers worry that it nonetheless lacks some crucial connection between theory and experiment. Such worries constitute the Quantum Measurement Problems. One can broadly identify two kinds of worries: (1) pragmatic: it is unclear how to model our measurement processes in order to extract experimental predictions, and (2) realist: we lack a satisfying metaphysical account of measurement processes. While both issues deserve attention, the pragmatic worries have worse consequences if left unanswered: If our pragmatic theory-to-experiment linkage is unsatisfactory, then quantum theory is at risk of losing both its evidential support and its physical salience. Avoiding these risks is at the core of what I will call thePragmatic Measurement Problem. Fortunately, the pragmatic measurement problem is not too difficult to solve. For non-relativistic quantum theory, the story goes roughly as follows: One can model each of quantum theory’s key experimental successes on a case-by-case basis by using a measurement chain. In modeling this measurement chain, it is pragmatically necessary to switch from using a quantum model to a classical model at some point. That is, it is pragmatically necessary to invoke a Heisenberg cut at some point along the measurement chain. Past this case-by-case measurement framework, one can then strive for a wide-scoping measurement theory capable of modeling all (or nearly all) possible measurement processes. For non-relativistic quantum theory, this leads us to our usual projective measurement theory. As a bonus, proceeding this way also gives us an empirically meaningful characterization of the theory’s observables as (positive) self-adjoint operators. But how does this story have to change when we move into the context of quantum field theory (QFT)? It is well known that in QFT almost all localized projective measurements violate causality, allowing for faster-than-light signaling; These are Sorkin’s impossible measurements. Thus, the story of measurement in QFT cannot end as it did before with a projective measurement theory. But does this then mean that we need to radically rethink the way we model measurement processes in QFT? Are our current experimental practices somehow misguided? Fortunately not. I will argue that (once properly understood) our old approach to modeling quantum measurements is still applicable in QFT contexts. We ought to first use measurement chains to build up a case-by-case measurement framework for QFT. Modeling these measurement chains will require us to invoke what I will call a QFT-cut. That is, at some point along the measurement chain we must switch from using a QFT model to a non-QFT model. Past this case-by-case measurement framework, we can then strive for both a new wide-scoping measurement theory for QFT and an empirically meaningful characterization of its observables. It is at this point that significantly more theoretical work is needed. This paper ends by briefly reviewing the state of the art in the physics literature regarding the modeling of measurement processes involving quantum fields.