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12:00

k-block-positivity is an important concept in quantum entanglement theory. A k-block-positive operator serves as a witness for states with Schmidt number k. It is also closely related to key notions such as bound entanglement and the distillability of entanglement, exemplified by the 2-copy distillability conjecture. However, determining whether a Hermitian operator is k-block-positive remains a challenging problem. In this talk, we reformulate the testing problem as an optimization problem, which is then incorporated into the semidefinite programming (SDP) framework. The number of SDP variables involved is substantial. To alleviate this, we explore symmetry-reduced SDP based on Schur-Weyl duality. Furthermore, we apply representation theory to estimate the number of SDP variables required for this algorithm, offering insights into hierarchy collapse in extreme cases.

https://combalgo.labri.fr/pmwiki.php/Groupe/Info-Quantique

Room 073