Commutative POVMs are smearing of spectral measures with the smearing realized by a Markov kernel. In the case of POVMs defined on the Borel σ-algebra of the reals, the existence of a universal Markov kernel has been established. Here we show that every weak Markov kernel is functionally subordinated to the universal Markov kernel. Then, we analyze the implications of that result to the characterization of a Markov kernel as a Choquet’s integral on the space of deterministic Markov kernels.

Universal Randomization of Quantum Observables

Beneduci, Roberto
2019

Abstract

Commutative POVMs are smearing of spectral measures with the smearing realized by a Markov kernel. In the case of POVMs defined on the Borel σ-algebra of the reals, the existence of a universal Markov kernel has been established. Here we show that every weak Markov kernel is functionally subordinated to the universal Markov kernel. Then, we analyze the implications of that result to the characterization of a Markov kernel as a Choquet’s integral on the space of deterministic Markov kernels.
Positive operator valued measures, Markov kernels, von Neumann algebras, Choquet’s integral, Quantum mechanics, Joint measurability
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/292993
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact