Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames
Protocols of quantum information science often realize in terms of specially selected states. In particular, such states are used to perform measurements at the final stage of a protocol. This study aims to explore measurements assigned to a mutually unbiased-equiangular tight frame. The utilized me...
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AIP Publishing LLC
2025-06-01
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| Series: | APL Quantum |
| Online Access: | http://dx.doi.org/10.1063/5.0254873 |
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| author | Alexey E. Rastegin |
| author_facet | Alexey E. Rastegin |
| author_sort | Alexey E. Rastegin |
| collection | DOAJ |
| description | Protocols of quantum information science often realize in terms of specially selected states. In particular, such states are used to perform measurements at the final stage of a protocol. This study aims to explore measurements assigned to a mutually unbiased-equiangular tight frame. The utilized method deals with Kirkwood–Dirac quasiprobabilities, which are increasingly used in contemporary research. These quasiprobabilities constitute a matrix that can be linked to unravelings of certain quantum channels. Using states of the given frame to build principal Kraus operators leads to quasiprobabilities that represent the measured state. The structure of a mutually unbiased-equiangular tight frame allows one to characterize entropies associated with a particular unraveling. To do this, we estimate some of the Schatten and Ky Fan norms of the matrix consisted of quasiprobabilities. New uncertainty relations in terms of Rényi and Tsallis entropies follow from the obtained inequalities. A utility of the presented inequalities is exemplified with mutually unbiased bases of a qubit and equiangular tight frames of a ququart. |
| format | Article |
| id | doaj-art-47e68b1a8fea42feac4f985e51c6b5ad |
| institution | Kabale University |
| issn | 2835-0103 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Quantum |
| spelling | doaj-art-47e68b1a8fea42feac4f985e51c6b5ad2025-08-20T03:29:17ZengAIP Publishing LLCAPL Quantum2835-01032025-06-0122026108026108-1210.1063/5.0254873Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight framesAlexey E. Rastegin0Irkutsk State University, K. Marx St. 1, Irkutsk 664003, RussiaProtocols of quantum information science often realize in terms of specially selected states. In particular, such states are used to perform measurements at the final stage of a protocol. This study aims to explore measurements assigned to a mutually unbiased-equiangular tight frame. The utilized method deals with Kirkwood–Dirac quasiprobabilities, which are increasingly used in contemporary research. These quasiprobabilities constitute a matrix that can be linked to unravelings of certain quantum channels. Using states of the given frame to build principal Kraus operators leads to quasiprobabilities that represent the measured state. The structure of a mutually unbiased-equiangular tight frame allows one to characterize entropies associated with a particular unraveling. To do this, we estimate some of the Schatten and Ky Fan norms of the matrix consisted of quasiprobabilities. New uncertainty relations in terms of Rényi and Tsallis entropies follow from the obtained inequalities. A utility of the presented inequalities is exemplified with mutually unbiased bases of a qubit and equiangular tight frames of a ququart.http://dx.doi.org/10.1063/5.0254873 |
| spellingShingle | Alexey E. Rastegin Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames APL Quantum |
| title | Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames |
| title_full | Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames |
| title_fullStr | Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames |
| title_full_unstemmed | Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames |
| title_short | Kirkwood–Dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames |
| title_sort | kirkwood dirac quasiprobabilities for measurements related to mutually unbiased equiangular tight frames |
| url | http://dx.doi.org/10.1063/5.0254873 |
| work_keys_str_mv | AT alexeyerastegin kirkwooddiracquasiprobabilitiesformeasurementsrelatedtomutuallyunbiasedequiangulartightframes |