تقرير
Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights
| العنوان: | Unveiling NPT bound problem: From Distillability Sets to Inequalities and Multivariable Insights |
|---|---|
| المؤلفون: | Qi, Si-Yuan, Gupur, Geni, Wu, Yu-Chun, Guo, Guo-Ping |
| المصدر: | Phys. Rev. A Vol. 110, Iss. 1 012406 (2024) |
| سنة النشر: | 2024 |
| المجموعة: | Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics |
| الوصف: | 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. Comment: 12 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevA.110.012406 |
| URL الوصول: | http://arxiv.org/abs/2402.18037 |
| رقم الأكسشن: | edsarx.2402.18037 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevA.110.012406 |
|---|