A formalism for steering with local quantum measurements
We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signallin...
| Main Authors: | , , , , |
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| Format: | Journal article |
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Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft
2018
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| _version_ | 1797063531936350208 |
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| author | Sainz, A Aolita, L Piani, M Hoban, M Skrzypczyk, P |
| author_facet | Sainz, A Aolita, L Piani, M Hoban, M Skrzypczyk, P |
| author_sort | Sainz, A |
| collection | OXFORD |
| description | We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone. |
| first_indexed | 2024-03-06T21:01:14Z |
| format | Journal article |
| id | oxford-uuid:3af3181c-95e7-470d-baad-c42081ed998a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:01:14Z |
| publishDate | 2018 |
| publisher | Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft |
| record_format | dspace |
| spelling | oxford-uuid:3af3181c-95e7-470d-baad-c42081ed998a2022-03-26T14:04:41ZA formalism for steering with local quantum measurementsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3af3181c-95e7-470d-baad-c42081ed998aSymplectic Elements at OxfordInstitute of Physics (IoP) and Deutsche Physikalische Gesellschaft2018Sainz, AAolita, LPiani, MHoban, MSkrzypczyk, PWe develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone. |
| spellingShingle | Sainz, A Aolita, L Piani, M Hoban, M Skrzypczyk, P A formalism for steering with local quantum measurements |
| title | A formalism for steering with local quantum measurements |
| title_full | A formalism for steering with local quantum measurements |
| title_fullStr | A formalism for steering with local quantum measurements |
| title_full_unstemmed | A formalism for steering with local quantum measurements |
| title_short | A formalism for steering with local quantum measurements |
| title_sort | formalism for steering with local quantum measurements |
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