Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements
While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for de...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/3/350 |
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| author | Jakub J. Borkała Chellasamy Jebarathinam Shubhayan Sarkar Remigiusz Augusiak |
| author_facet | Jakub J. Borkała Chellasamy Jebarathinam Shubhayan Sarkar Remigiusz Augusiak |
| author_sort | Jakub J. Borkała |
| collection | DOAJ |
| description | While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><msub><mo form="prefix">log</mo><mn>2</mn></msub><mn>3</mn></mrow></semantics></math></inline-formula> random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit a device-independent method for certification of the full Weyl–Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states. |
| first_indexed | 2024-03-09T19:51:51Z |
| format | Article |
| id | doaj.art-118b7ed861cd444293b79cd4301d9322 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T19:51:51Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-118b7ed861cd444293b79cd4301d93222023-11-24T01:07:08ZengMDPI AGEntropy1099-43002022-02-0124335010.3390/e24030350Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective MeasurementsJakub J. Borkała0Chellasamy Jebarathinam1Shubhayan Sarkar2Remigiusz Augusiak3Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, PolandCenter for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, PolandCenter for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, PolandCenter for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, PolandWhile it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><msub><mo form="prefix">log</mo><mn>2</mn></msub><mn>3</mn></mrow></semantics></math></inline-formula> random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit a device-independent method for certification of the full Weyl–Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states.https://www.mdpi.com/1099-4300/24/3/350randomness certificationself-testingextremal POVMWeyl–Heisenberg basis |
| spellingShingle | Jakub J. Borkała Chellasamy Jebarathinam Shubhayan Sarkar Remigiusz Augusiak Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements Entropy randomness certification self-testing extremal POVM Weyl–Heisenberg basis |
| title | Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements |
| title_full | Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements |
| title_fullStr | Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements |
| title_full_unstemmed | Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements |
| title_short | Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements |
| title_sort | device independent certification of maximal randomness from pure entangled two qutrit states using non projective measurements |
| topic | randomness certification self-testing extremal POVM Weyl–Heisenberg basis |
| url | https://www.mdpi.com/1099-4300/24/3/350 |
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