Borsten, L. and Jubb, I. and Kells, Graham (2021) Impossible measurements revisited. Physical Review D, 104 (2). ISSN 2470-0029

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Abstract

It is by now well recognized that the naive application of the projection postulate on composite quantum systems can induce signalling between their constituent components, indicative of a breakdown of causality in a relativistic spacetime context. Here we introduce a necessary and sufficient condition for an ideal measurement of an observable to be nonsignalling. As well as being particularly simple, it generalizes previous no-signalling conditions in that it allows for degeneracies and can be applied to all bounded selfadjoint operators. The condition is used to establish that arbitrary sums of local observables will not signal, in accordance with our expectations from relativistic quantum field theory. On the other hand, it is shown that the measurement of the tensor product of commuting local observables, for example bipartite operators of the form A ⊗ B, can in fact signal, contrary to the widely held belief that such measurements are always locally realizable. The implications for the notion of measurement in relativistic quantum field theory are addressed; it appears that the most straightforward application of the standard quantum formalism generically leads to violations of causality. We conclude that either the class of observables that can be measured should be restricted and/or that the naive translation of the measurement framework of quantum theory, in particular the projection postulate, to quantum field theory should be reevaluated.

Item Type:	Article
Keywords:	quantum field theory; measurement; causality; projection postulate;
Academic Unit:	Faculty of Science and Engineering > Theoretical Physics
Item ID:	18415
Identification Number:	https://doi.org/10.1103/PhysRevD.104.025012
Depositing User:	Graham Kells
Date Deposited:	22 Apr 2024 13:40
Journal or Publication Title:	Physical Review D
Publisher:	American Physical Society
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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