On the structure of mirrored operators obtained from optimal entanglement witnesses
Abstract Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin—a mirrored EW—whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-37771-0 |
| _version_ | 1797784682688937984 |
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| author | Anindita Bera Joonwoo Bae Beatrix C. Hiesmayr Dariusz Chruściński |
| author_facet | Anindita Bera Joonwoo Bae Beatrix C. Hiesmayr Dariusz Chruściński |
| author_sort | Anindita Bera |
| collection | DOAJ |
| description | Abstract Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin—a mirrored EW—whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem. |
| first_indexed | 2024-03-13T00:43:23Z |
| format | Article |
| id | doaj.art-30b4bfa1c56b49f68dc50419178efe70 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-13T00:43:23Z |
| publishDate | 2023-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-30b4bfa1c56b49f68dc50419178efe702023-07-09T11:10:50ZengNature PortfolioScientific Reports2045-23222023-07-0113111510.1038/s41598-023-37771-0On the structure of mirrored operators obtained from optimal entanglement witnessesAnindita Bera0Joonwoo Bae1Beatrix C. Hiesmayr2Dariusz Chruściński3Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus UniversitySchool of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST)Faculty of Physics, University of ViennaInstitute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus UniversityAbstract Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin—a mirrored EW—whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.https://doi.org/10.1038/s41598-023-37771-0 |
| spellingShingle | Anindita Bera Joonwoo Bae Beatrix C. Hiesmayr Dariusz Chruściński On the structure of mirrored operators obtained from optimal entanglement witnesses Scientific Reports |
| title | On the structure of mirrored operators obtained from optimal entanglement witnesses |
| title_full | On the structure of mirrored operators obtained from optimal entanglement witnesses |
| title_fullStr | On the structure of mirrored operators obtained from optimal entanglement witnesses |
| title_full_unstemmed | On the structure of mirrored operators obtained from optimal entanglement witnesses |
| title_short | On the structure of mirrored operators obtained from optimal entanglement witnesses |
| title_sort | on the structure of mirrored operators obtained from optimal entanglement witnesses |
| url | https://doi.org/10.1038/s41598-023-37771-0 |
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