Order preserving maps on quantum measurements
We study the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. The post-processing order is fundamental as it enables to compare measurements by their intrinsic noise and it gives grounds to define the important concept of quantum in...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2022-11-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2022-11-10-853/pdf/ |
| _version_ | 1811232747393384448 |
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| author | Teiko Heinosaari Maria Anastasia Jivulescu Ion Nechita |
| author_facet | Teiko Heinosaari Maria Anastasia Jivulescu Ion Nechita |
| author_sort | Teiko Heinosaari |
| collection | DOAJ |
| description | We study the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. The post-processing order is fundamental as it enables to compare measurements by their intrinsic noise and it gives grounds to define the important concept of quantum incompatibility. Our approach is based on mapping this set into a simpler partially ordered set using an order preserving map and investigating the resulting image. The aim is to ignore unnecessary details while keeping the essential structure, thereby simplifying e.g. detection of incompatibility. One possible choice is the map based on Fisher information introduced by Huangjun Zhu, known to be an order morphism taking values in the cone of positive semidefinite matrices. We explore the properties of that construction and improve Zhu's incompatibility criterion by adding a constraint depending on the number of measurement outcomes. We generalize this type of construction to other ordered vector spaces and we show that this map is optimal among all quadratic maps. |
| first_indexed | 2024-04-12T11:09:26Z |
| format | Article |
| id | doaj.art-af668f7c11b94bd3a44da68ebf6ac82c |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-12T11:09:26Z |
| publishDate | 2022-11-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-af668f7c11b94bd3a44da68ebf6ac82c2022-12-22T03:35:40ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2022-11-01685310.22331/q-2022-11-10-85310.22331/q-2022-11-10-853Order preserving maps on quantum measurementsTeiko HeinosaariMaria Anastasia JivulescuIon NechitaWe study the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. The post-processing order is fundamental as it enables to compare measurements by their intrinsic noise and it gives grounds to define the important concept of quantum incompatibility. Our approach is based on mapping this set into a simpler partially ordered set using an order preserving map and investigating the resulting image. The aim is to ignore unnecessary details while keeping the essential structure, thereby simplifying e.g. detection of incompatibility. One possible choice is the map based on Fisher information introduced by Huangjun Zhu, known to be an order morphism taking values in the cone of positive semidefinite matrices. We explore the properties of that construction and improve Zhu's incompatibility criterion by adding a constraint depending on the number of measurement outcomes. We generalize this type of construction to other ordered vector spaces and we show that this map is optimal among all quadratic maps.https://quantum-journal.org/papers/q-2022-11-10-853/pdf/ |
| spellingShingle | Teiko Heinosaari Maria Anastasia Jivulescu Ion Nechita Order preserving maps on quantum measurements Quantum |
| title | Order preserving maps on quantum measurements |
| title_full | Order preserving maps on quantum measurements |
| title_fullStr | Order preserving maps on quantum measurements |
| title_full_unstemmed | Order preserving maps on quantum measurements |
| title_short | Order preserving maps on quantum measurements |
| title_sort | order preserving maps on quantum measurements |
| url | https://quantum-journal.org/papers/q-2022-11-10-853/pdf/ |
| work_keys_str_mv | AT teikoheinosaari orderpreservingmapsonquantummeasurements AT mariaanastasiajivulescu orderpreservingmapsonquantummeasurements AT ionnechita orderpreservingmapsonquantummeasurements |