The notion of observable and the moment problem for $$*$$-algebras and their GNS representations

Drago, Nicolò; Moretti, Valter

doi:10.1007/s11005-020-01277-x

Cited by 9 publications

(4 citation statements)

References 22 publications

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“…A state on a theory (or simply on a unital * -algebra A) is a linear map ω : A → C which is normalised, i.e., ω(1 1) = 1 and positive, i.e., ∀A ∈ A : ω(A † A) ≥ 0. We interpret it to assign expectation values to observables, see also [29]. If the algebra elements are represented as operators on a Hilbert space, then a state ω could be of the from ω(A) = Tr (ρ ω A) for a "density matrix" ρ ω .…”

Section: Algebraic Quantum Field Theorymentioning

confidence: 99%

Weakly coupled local particle detectors cannot harvest entanglement

Ruep

2021

Preprint

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Many states of linear real scalar quantum fields (in particular Reeh-Schlieder states) on flat as well as curved spacetime are entangled on spacelike separated local algebras of observables. It has been argued that this entanglement can be "harvested" by a pair of so-called particle detectors, for example singularly or non-locally coupled quantum mechanical harmonic oscillator Unruh detectors. In an attempt to avoid such imperfect coupling, we analyse a model-independent local and covariant entanglement harvesting protocol based on the local probes of a recently proposed measurement theory of quantum fields. We then introduce the notion of a local particle detector concretely given by a local mode of a linear real scalar probe field on possibly curved spacetime and possibly under the influence of external fields. In a non-perturbative analysis we find that local particle detectors cannot harvest entanglement below a critical coupling strength when the corresponding probe fields are initially prepared in quasi-free Reeh-Schlieder states and are coupled to a system field prepared in a quasi-free state. This is a consequence of the fact that Reeh-Schlieder states restrict to truly mixed states on any local mode.

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Section: Algebraic Quantum Field Theorymentioning

confidence: 99%

Weakly coupled local particle detectors cannot harvest entanglement

Ruep

2021

Preprint

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“…For an analysis of the interpretation in terms of the first moment of an underlying probability measure we refer the reader to [11]. The induced system observable Z ρ P corresponding to probe observable Z is, by definition, the observable whose expectation in state ρ S matches that of the actual experiment:…”

Section: Introductionmentioning

confidence: 99%

Impossible measurements require impossible apparatus

2021

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A well-recognised open conceptual problem in relativistic quantum field theory concerns the relation between measurement and causality. Naive generalisations of quantum measurement rules can allow for superluminal signalling ('impossible measurements'). This raises the problem of delineating physically allowed quantum measurements and operations. We analyse this issue in a recently proposed framework in which local measurements (in possibly curved spacetime) are described physically by coupling the system to a probe. We show that the state-update rule in this setting is consistent with causality provided that the coupling between the system and probe is local. Thus, by establishing a well-defined framework for successive measurements, we also provide a class of physically allowed operations. Conversely, impossible measurements can only be performed using impossible (non-local) apparatus.

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“…∀ A ∈ A : ω(A † A) 0. We interpret it to assign expectation values to observables, see also [36]. If the algebra elements are represented as operators on a Hilbert space, then a state ω could be of the from ω(A) = Tr (ρ ω A) for a 'density matrix' ρ ω .…”

Section: Algebraic Quantum Field Theorymentioning

confidence: 99%

Weakly coupled local particle detectors cannot harvest entanglement

Ruep

2021

Class. Quantum Grav.

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Many states of linear real scalar quantum fields (in particular Reeh–Schlieder states) on flat as well as curved spacetime are entangled on spacelike separated local algebras of observables. It has been argued that this entanglement can be ‘harvested’ by a pair of so-called particle detectors, for example singularly or non-locally coupled quantum mechanical harmonic oscillator Unruh detectors. In an attempt to avoid such imperfect coupling, we analyse a model-independent local and covariant entanglement harvesting protocol based on the local probes of a recently proposed measurement theory of quantum fields. We then introduce the notion of a local particle detector concretely given by a local mode of a linear real scalar probe field on possibly curved spacetime and possibly under the influence of external fields. In a non-perturbative analysis we find that local particle detectors cannot harvest entanglement below a critical coupling strength when the corresponding probe fields are initially prepared in quasi-free Reeh–Schlieder states and are coupled to a system field prepared in a quasi-free state. This is a consequence of the fact that Reeh–Schlieder states restrict to truly mixed states on any local mode.

show abstract

The notion of observable and the moment problem for $$*$$-algebras and their GNS representations

Cited by 9 publications

References 22 publications

Weakly coupled local particle detectors cannot harvest entanglement

Weakly coupled local particle detectors cannot harvest entanglement

Impossible measurements require impossible apparatus

Weakly coupled local particle detectors cannot harvest entanglement

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