Entanglement measures and LOCC conversion criteria from Schur-Weyl duality
Abstract
The characterization of possible transformations between quantum states and the quantification of entanglement are central for understanding quantum resources. Explicit results are, however, scarce since they require complicated optimizations over transformation protocols or state decompositions. We introduce a method to optimize functions of the entanglement spectrum of bipartite states over mixed-state decompositions with arbitrary accuracy. Our results are based on a convergent semidefinite programming hierarchy of optimizations over entanglement spectra using a natural polynomial basis and Schur-Weyl duality. Our approach can also be used to determine non-polynomial measures, such as the entanglement of formation, and to characterize the dimensionality of entanglement. Moreover, extracting the decomposition allows us to formulate criteria to determine state transformations under local operations and classical communication (LOCC). In particular, we provide a hierarchy of certificates of LOCC non-convertibility from pure to mixed states in any dimension and a heuristic approach for LOCC convertibility.
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BibTeX
@misc{cleemput2026entanglement,
title = {{Entanglement measures and LOCC conversion criteria from Schur-Weyl duality}},
author = {Anton van Cleemput and Otfried Gühne and Albert Rico},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37785},
eprint = {2610.37785},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37785},
}
RIS
TY - UNPB
TI - Entanglement measures and LOCC conversion criteria from Schur-Weyl duality
AU - Anton van Cleemput
AU - Otfried Gühne
AU - Albert Rico
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37785
UR - https://arxiv.org/abs/2610.37785
AB - The characterization of possible transformations between quantum states and the quantification of entanglement are central for understanding quantum resources. Explicit results are, however, scarce since they require complicated optimizations over transformation protocols or state decompositions. We introduce a method to optimize functions of the entanglement spectrum of bipartite states over mixed-state decompositions with arbitrary accuracy. Our results are based on a convergent semidefinite programming hierarchy of optimizations over entanglement spectra using a natural polynomial basis and Schur-Weyl duality. Our approach can also be used to determine non-polynomial measures, such as the entanglement of formation, and to characterize the dimensionality of entanglement. Moreover, extracting the decomposition allows us to formulate criteria to determine state transformations under local operations and classical communication (LOCC). In particular, we provide a hierarchy of certificates of LOCC non-convertibility from pure to mixed states in any dimension and a heuristic approach for LOCC convertibility.
ER -