On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states
Hereunder, we study the class of irreducible private states that are private states from which all the secret content is accessible via measuring their key part. We provide the first protocol which distills key not only from the key part, but also from the shield if only the state is reducible. We p...
| 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 |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aad75a |
| _version_ | 1797750616605327360 |
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| author | K Horodecki P Ćwikliński A Rutkowski M Studziński |
| author_facet | K Horodecki P Ćwikliński A Rutkowski M Studziński |
| author_sort | K Horodecki |
| collection | DOAJ |
| description | Hereunder, we study the class of irreducible private states that are private states from which all the secret content is accessible via measuring their key part. We provide the first protocol which distills key not only from the key part, but also from the shield if only the state is reducible. We prove also a tighter upper bound on the performance of that protocol, given in terms of regularized relative entropy of entanglement instead of relative entropy of entanglement previously known. This implies in particular that the irreducible private states are all strictly irreducible if and only if the entangled but key-undistillable states (‘entangled key-undistilable states’) exist. In turn, all the irreducible private states of the dimension 4 ⨂ 4 are strictly irreducible, that is, after an attack on the key part they become separable. Provided the bound key states exist, we consider different subclasses of the irreducible private states and their properties. Finally we provide a lower bound on the trace norm distance between key-undistillable states and private states, in sufficiently high dimensions. |
| first_indexed | 2024-03-12T16:35:25Z |
| format | Article |
| id | doaj.art-539c465f9aa34ca8834071f01e2b832d |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:25Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-539c465f9aa34ca8834071f01e2b832d2023-08-08T14:53:16ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120808302110.1088/1367-2630/aad75aOn distilling secure key from reducible private states and (non)existence of entangled key-undistillable statesK Horodecki0P Ćwikliński1A Rutkowski2M Studziński3https://orcid.org/0000-0002-5946-9845Institute of Informatics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdańsk , 80–308 Gdańsk, PolandInstitute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdańsk , 80–308 Gdańsk, PolandInstitute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdańsk , 80–308 Gdańsk, PolandDAMTP, Centre for Mathematical Sciences, University of Cambridge , Cambridge CB30WA, United KingdomHereunder, we study the class of irreducible private states that are private states from which all the secret content is accessible via measuring their key part. We provide the first protocol which distills key not only from the key part, but also from the shield if only the state is reducible. We prove also a tighter upper bound on the performance of that protocol, given in terms of regularized relative entropy of entanglement instead of relative entropy of entanglement previously known. This implies in particular that the irreducible private states are all strictly irreducible if and only if the entangled but key-undistillable states (‘entangled key-undistilable states’) exist. In turn, all the irreducible private states of the dimension 4 ⨂ 4 are strictly irreducible, that is, after an attack on the key part they become separable. Provided the bound key states exist, we consider different subclasses of the irreducible private states and their properties. Finally we provide a lower bound on the trace norm distance between key-undistillable states and private states, in sufficiently high dimensions.https://doi.org/10.1088/1367-2630/aad75aprivate statesirreducible private stateskey distillationbound key states |
| spellingShingle | K Horodecki P Ćwikliński A Rutkowski M Studziński On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states New Journal of Physics private states irreducible private states key distillation bound key states |
| title | On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states |
| title_full | On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states |
| title_fullStr | On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states |
| title_full_unstemmed | On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states |
| title_short | On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states |
| title_sort | on distilling secure key from reducible private states and non existence of entangled key undistillable states |
| topic | private states irreducible private states key distillation bound key states |
| url | https://doi.org/10.1088/1367-2630/aad75a |
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