Two-qubit causal structures and the geometry of positive qubit-maps
We study quantum causal inference in a setup proposed by Ried et al (2015 Nat. Phys. 11 414) in which a common cause scenario can be mixed with a cause–effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: whereas in classical...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/aad612 |
| _version_ | 1797750618598670336 |
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| author | Jonas M Kübler Daniel Braun |
| author_facet | Jonas M Kübler Daniel Braun |
| author_sort | Jonas M Kübler |
| collection | DOAJ |
| description | We study quantum causal inference in a setup proposed by Ried et al (2015 Nat. Phys. 11 414) in which a common cause scenario can be mixed with a cause–effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit channels and steering maps. We find the range of mixing parameters that can generate given correlations, and prove a quantum advantage in a more general setup, allowing arbitrary unital channels and initial states with fully mixed reduced states. This is achieved by establishing new bounds on signed singular values of sums of matrices. Based on the geometry, we quantify and identify the origin of the quantum advantage depending on the observed correlations, and discuss how additional constraints can lead to a unique solution of the problem. |
| first_indexed | 2024-03-12T16:36:23Z |
| format | Article |
| id | doaj.art-5c73df0eb9be4d55961e7d366eea48cc |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:36:23Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-5c73df0eb9be4d55961e7d366eea48cc2023-08-08T14:52:01ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120808301510.1088/1367-2630/aad612Two-qubit causal structures and the geometry of positive qubit-mapsJonas M Kübler0Daniel Braun1https://orcid.org/0000-0001-8598-2039Institut für Theoretische Physik, Universität Tübingen , D-72076 Tübingen, GermanyInstitut für Theoretische Physik, Universität Tübingen , D-72076 Tübingen, GermanyWe study quantum causal inference in a setup proposed by Ried et al (2015 Nat. Phys. 11 414) in which a common cause scenario can be mixed with a cause–effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit channels and steering maps. We find the range of mixing parameters that can generate given correlations, and prove a quantum advantage in a more general setup, allowing arbitrary unital channels and initial states with fully mixed reduced states. This is achieved by establishing new bounds on signed singular values of sums of matrices. Based on the geometry, we quantify and identify the origin of the quantum advantage depending on the observed correlations, and discuss how additional constraints can lead to a unique solution of the problem.https://doi.org/10.1088/1367-2630/aad612quantum causal inferencequantum informationpositive qubit-mapssigned singular values |
| spellingShingle | Jonas M Kübler Daniel Braun Two-qubit causal structures and the geometry of positive qubit-maps New Journal of Physics quantum causal inference quantum information positive qubit-maps signed singular values |
| title | Two-qubit causal structures and the geometry of positive qubit-maps |
| title_full | Two-qubit causal structures and the geometry of positive qubit-maps |
| title_fullStr | Two-qubit causal structures and the geometry of positive qubit-maps |
| title_full_unstemmed | Two-qubit causal structures and the geometry of positive qubit-maps |
| title_short | Two-qubit causal structures and the geometry of positive qubit-maps |
| title_sort | two qubit causal structures and the geometry of positive qubit maps |
| topic | quantum causal inference quantum information positive qubit-maps signed singular values |
| url | https://doi.org/10.1088/1367-2630/aad612 |
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