Incompatibility of quantum instruments
Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system, generalizes incompatibility of channels and incompatibility of po...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-02-12-1246/pdf/ |
| _version_ | 1797316408086888448 |
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| author | Leevi Leppäjärvi Michal Sedlák |
| author_facet | Leevi Leppäjärvi Michal Sedlák |
| author_sort | Leevi Leppäjärvi |
| collection | DOAJ |
| description | Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system, generalizes incompatibility of channels and incompatibility of positive operator-valued measures (POVMs). We derive implications of instrument compatibility for the induced POVMs and channels. We also study relation of instrument compatibility to the concept of non-disturbance. Finally, we prove equivalence between instrument compatibility and postprocessing of certain instruments, which we term complementary instruments. We illustrate our findings on examples of various classes of instruments. |
| first_indexed | 2024-03-08T03:17:57Z |
| format | Article |
| id | doaj.art-bab6d7770e6d417b841bce435bb1035e |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-08T03:17:57Z |
| publishDate | 2024-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-bab6d7770e6d417b841bce435bb1035e2024-02-12T13:54:09ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-02-018124610.22331/q-2024-02-12-124610.22331/q-2024-02-12-1246Incompatibility of quantum instrumentsLeevi LeppäjärviMichal SedlákQuantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system, generalizes incompatibility of channels and incompatibility of positive operator-valued measures (POVMs). We derive implications of instrument compatibility for the induced POVMs and channels. We also study relation of instrument compatibility to the concept of non-disturbance. Finally, we prove equivalence between instrument compatibility and postprocessing of certain instruments, which we term complementary instruments. We illustrate our findings on examples of various classes of instruments.https://quantum-journal.org/papers/q-2024-02-12-1246/pdf/ |
| spellingShingle | Leevi Leppäjärvi Michal Sedlák Incompatibility of quantum instruments Quantum |
| title | Incompatibility of quantum instruments |
| title_full | Incompatibility of quantum instruments |
| title_fullStr | Incompatibility of quantum instruments |
| title_full_unstemmed | Incompatibility of quantum instruments |
| title_short | Incompatibility of quantum instruments |
| title_sort | incompatibility of quantum instruments |
| url | https://quantum-journal.org/papers/q-2024-02-12-1246/pdf/ |
| work_keys_str_mv | AT leevileppajarvi incompatibilityofquantuminstruments AT michalsedlak incompatibilityofquantuminstruments |