Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.18037 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914853861457920 |
|---|---|
| author | Qi, Si-Yuan Gupur, Geni Wu, Yu-Chun Guo, Guo-Ping |
| author_facet | Qi, Si-Yuan Gupur, Geni Wu, Yu-Chun Guo, Guo-Ping |
| contents | Equivalence between Positive Partial Transpose (PPT) entanglement and bound entanglement is a long-standing open problem in quantum information theory. So far limited progress has been made, even on the seemingly simple case of Werner states bound entanglement. The primary challenge is to give a concise mathematical representation of undistillability. To this end, we propose a decomposition of the N-undistillability verification into $log(N)$ repeated steps of 1-undistillability verification. For Werner state N-undistillability verification, a bound for N-undistillability is given, which is independent of the dimensionality of Werner states. Equivalent forms of inequalities for both rank one and two matrices are presented, before transforming the two-undistillability case into a matrix analysis problem. A new perspective is also attempted by seeing it as a non-convex multi-variable function, proving its critical points and conjecturing Hessian positivity, which would make them local minimums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights Qi, Si-Yuan Gupur, Geni Wu, Yu-Chun Guo, Guo-Ping Quantum Physics Equivalence between Positive Partial Transpose (PPT) entanglement and bound entanglement is a long-standing open problem in quantum information theory. So far limited progress has been made, even on the seemingly simple case of Werner states bound entanglement. The primary challenge is to give a concise mathematical representation of undistillability. To this end, we propose a decomposition of the N-undistillability verification into $log(N)$ repeated steps of 1-undistillability verification. For Werner state N-undistillability verification, a bound for N-undistillability is given, which is independent of the dimensionality of Werner states. Equivalent forms of inequalities for both rank one and two matrices are presented, before transforming the two-undistillability case into a matrix analysis problem. A new perspective is also attempted by seeing it as a non-convex multi-variable function, proving its critical points and conjecturing Hessian positivity, which would make them local minimums. |
| title | Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.18037 |