A class of entanglement witnesses and a realignment-like criterion
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917868079153152 |
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| author | Jannesary, Vahid Karimipour, Vahid Chruściński, Dariusz |
| author_facet | Jannesary, Vahid Karimipour, Vahid Chruściński, Dariusz |
| contents | We present a multi-parameter family of positive maps between spaces of differing dimensions. This framework facilitates the construction of Entanglement Witnesses (EWs) specifically designed for systems living in $d_1 \times d_2$ dimensions. A sufficient condition for positivity is presented. Interestingly, it is shown that all EWs constructed this way are equivalent to a single realignment-like criterion which for $d_1 \neq d_2$ is in general stronger than the original realignment criterion. We illustrate effectiveness of this criterion considering examples of Positive Partial Transpose (PPT) entangled states in $3 \times 3$ and $3 \times 4$ dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07019 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A class of entanglement witnesses and a realignment-like criterion Jannesary, Vahid Karimipour, Vahid Chruściński, Dariusz Quantum Physics We present a multi-parameter family of positive maps between spaces of differing dimensions. This framework facilitates the construction of Entanglement Witnesses (EWs) specifically designed for systems living in $d_1 \times d_2$ dimensions. A sufficient condition for positivity is presented. Interestingly, it is shown that all EWs constructed this way are equivalent to a single realignment-like criterion which for $d_1 \neq d_2$ is in general stronger than the original realignment criterion. We illustrate effectiveness of this criterion considering examples of Positive Partial Transpose (PPT) entangled states in $3 \times 3$ and $3 \times 4$ dimensions. |
| title | A class of entanglement witnesses and a realignment-like criterion |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2308.07019 |