Research output: Contribution to journal › Article › peer-review

**Fewster-Verch2020_Article_QuantumFieldsAndLocalMeasureme**592 KB, PDF document

Journal | Communications in Mathematical Physics |
---|---|

Date | Accepted/In press - 30 Apr 2020 |

Date | E-pub ahead of print - 27 Jul 2020 |

Date | Published (current) - Sep 2020 |

Issue number | 2 |

Volume | 378 |

Number of pages | 39 |

Pages (from-to) | 851–889 |

Early online date | 27/07/20 |

Original language | English |

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.

Post-selected states conditioned on measurement outcomes are obtained using Davies-Lewis 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.

Post-selected states conditioned on measurement outcomes are obtained using Davies-Lewis 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.

© The Author(s) 2020

## Impossible measurements require impossible apparatus

Research output: Contribution to journal › Article › peer-review

## A generally covariant measurement scheme for quantum field theory in curved spacetimes

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

## Measurement and causality in quantum field theory

Activity: Talk or presentation › Invited talk

## Measurement schemes in local quantum physics

Activity: Talk or presentation › Invited talk

## Measurement schemes for quantum field theory in curved spacetimes

Activity: Talk or presentation › Invited talk

## Local measurement schemes for quantum field theory in curved spacetimes

Activity: Talk or presentation › Invited talk

## Progress and Visions in Quantum Theory in View of Gravity: Bridging foundations of physics and mathematics

Activity: Participating in or organising an event › Conference participation

## Rainer Verch

Activity: Hosting a visitor › Academic

Find related publications, people, projects, datasets and more using interactive charts.