Process Tomography in General Physical Theories

Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here, we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in general physical theories. Specifically, we explore the requ...

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Autor principal:	Giulio Chiribella
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	general probabilistic theories operational probabilistic theories process tomography dynamically faithful states universal extensions teleportation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a53226d8607b49a79c2e5460c38facdd
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spelling	oai:doaj.org-article:a53226d8607b49a79c2e5460c38facdd2021-11-25T19:05:46ZProcess Tomography in General Physical Theories10.3390/sym131119852073-8994https://doaj.org/article/a53226d8607b49a79c2e5460c38facdd2021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/1985https://doaj.org/toc/2073-8994Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here, we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in general physical theories. Specifically, we explore the requirement that process tomography should be achievable with a finite number of auxiliary systems and with a finite number of input states. We show that this requirement is satisfied in every theory equipped with universal extensions, that is, correlated states from which all other correlations can be generated locally with non-zero probability. We show that universal extensions are guaranteed to exist in two cases: (1) theories permitting conclusive state teleportation, and (2) theories satisfying three properties of Causality, Pure Product States, and Purification. In case (2), the existence of universal extensions follows from a symmetry property of Purification, whereby all pure bipartite states with the same marginal on one system are locally interconvertible. Crucially, our results hold even in theories that do not satisfy Local Tomography, the property that the state of any composite system can be identified from the correlations of local measurements. Summarizing, the existence of universal extensions, without any additional requirement of Local Tomography, is a sufficient guarantee for the characterizability of physical processes using a finite number of auxiliary systems and with a finite number of input systems.Giulio ChiribellaMDPI AGarticlegeneral probabilistic theoriesoperational probabilistic theoriesprocess tomographydynamically faithful statesuniversal extensionsteleportationMathematicsQA1-939ENSymmetry, Vol 13, Iss 1985, p 1985 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	general probabilistic theories operational probabilistic theories process tomography dynamically faithful states universal extensions teleportation Mathematics QA1-939
spellingShingle	general probabilistic theories operational probabilistic theories process tomography dynamically faithful states universal extensions teleportation Mathematics QA1-939 Giulio Chiribella Process Tomography in General Physical Theories
description	Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here, we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in general physical theories. Specifically, we explore the requirement that process tomography should be achievable with a finite number of auxiliary systems and with a finite number of input states. We show that this requirement is satisfied in every theory equipped with universal extensions, that is, correlated states from which all other correlations can be generated locally with non-zero probability. We show that universal extensions are guaranteed to exist in two cases: (1) theories permitting conclusive state teleportation, and (2) theories satisfying three properties of Causality, Pure Product States, and Purification. In case (2), the existence of universal extensions follows from a symmetry property of Purification, whereby all pure bipartite states with the same marginal on one system are locally interconvertible. Crucially, our results hold even in theories that do not satisfy Local Tomography, the property that the state of any composite system can be identified from the correlations of local measurements. Summarizing, the existence of universal extensions, without any additional requirement of Local Tomography, is a sufficient guarantee for the characterizability of physical processes using a finite number of auxiliary systems and with a finite number of input systems.
format	article
author	Giulio Chiribella
author_facet	Giulio Chiribella
author_sort	Giulio Chiribella
title	Process Tomography in General Physical Theories
title_short	Process Tomography in General Physical Theories
title_full	Process Tomography in General Physical Theories
title_fullStr	Process Tomography in General Physical Theories
title_full_unstemmed	Process Tomography in General Physical Theories
title_sort	process tomography in general physical theories
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/a53226d8607b49a79c2e5460c38facdd
work_keys_str_mv	AT giuliochiribella processtomographyingeneralphysicaltheories
_version_	1718410296377212928

Process Tomography in General Physical Theories

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