Units of rotational information
Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference....
| Main Authors: | , , |
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| Format: | Journal article |
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IOP Publishing
2017
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| _version_ | 1797098127671427072 |
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| author | Yang, Y Chiribella, G Hu, Q |
| author_facet | Yang, Y Chiribella, G Hu, Q |
| author_sort | Yang, Y |
| collection | OXFORD |
| description | Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin. |
| first_indexed | 2024-03-07T05:05:13Z |
| format | Journal article |
| id | oxford-uuid:d9b24ef9-0712-44fb-9013-b05fe18088c4 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:05:13Z |
| publishDate | 2017 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:d9b24ef9-0712-44fb-9013-b05fe18088c42022-03-27T08:57:47ZUnits of rotational informationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d9b24ef9-0712-44fb-9013-b05fe18088c4Symplectic Elements at OxfordIOP Publishing2017Yang, YChiribella, GHu, QEntanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin. |
| spellingShingle | Yang, Y Chiribella, G Hu, Q Units of rotational information |
| title | Units of rotational information |
| title_full | Units of rotational information |
| title_fullStr | Units of rotational information |
| title_full_unstemmed | Units of rotational information |
| title_short | Units of rotational information |
| title_sort | units of rotational information |
| work_keys_str_mv | AT yangy unitsofrotationalinformation AT chiribellag unitsofrotationalinformation AT huq unitsofrotationalinformation |