Optimal quantum networks and one-shot entropies
We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interative tests set up by a verifier. W...
| Main Authors: | , |
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| Format: | Journal article |
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IOP Publishing
2016
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| _version_ | 1826264571205124096 |
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| author | Chiribella, G Ebler, D |
| author_facet | Chiribella, G Ebler, D |
| author_sort | Chiribella, G |
| collection | OXFORD |
| description | We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interative tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game. |
| first_indexed | 2024-03-06T20:09:58Z |
| format | Journal article |
| id | oxford-uuid:2a385776-5a07-4487-a1d2-9f7ee7ccae56 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:09:58Z |
| publishDate | 2016 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:2a385776-5a07-4487-a1d2-9f7ee7ccae562022-03-26T12:23:47ZOptimal quantum networks and one-shot entropiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2a385776-5a07-4487-a1d2-9f7ee7ccae56Symplectic Elements at OxfordIOP Publishing2016Chiribella, GEbler, DWe develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interative tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game. |
| spellingShingle | Chiribella, G Ebler, D Optimal quantum networks and one-shot entropies |
| title | Optimal quantum networks and one-shot entropies |
| title_full | Optimal quantum networks and one-shot entropies |
| title_fullStr | Optimal quantum networks and one-shot entropies |
| title_full_unstemmed | Optimal quantum networks and one-shot entropies |
| title_short | Optimal quantum networks and one-shot entropies |
| title_sort | optimal quantum networks and one shot entropies |
| work_keys_str_mv | AT chiribellag optimalquantumnetworksandoneshotentropies AT eblerd optimalquantumnetworksandoneshotentropies |