A commuting operator self-test for exact entanglement embezzlement
Abstract
We show that the optimal commuting operator correlation for a variant of Coladangelo's two-player generalized nonlocal game, based on the embezzlement of entanglement, is a commuting operator self-test. Our result gives the first correlation self-test for an exact entanglement embezzlement protocol in the commuting operator framework. Because the unique optimal correlation necessitates the exact embezzlement of entanglement, the correlation is unrealizable using quantum tensor-product models, even if the local spaces are allowed to be infinite dimensional. As such, our result provides an example of a commuting operator self-test where the Hilbert space shared by the two parties cannot be factored into a tensor-product of local spaces that is compatible with the local measurement operators. Our main proof technique relies on Harris' unique abstract state characterization of exact embezzlement of entanglement involving Cuntz algebras.
Related
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BibTeX
@misc{paddock2026commuting,
title = {{A commuting operator self-test for exact entanglement embezzlement}},
author = {Connor Paddock and Simon Schmidt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38083},
eprint = {2609.38083},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38083},
}
RIS
TY - UNPB
TI - A commuting operator self-test for exact entanglement embezzlement
AU - Connor Paddock
AU - Simon Schmidt
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38083
UR - https://arxiv.org/abs/2609.38083
AB - We show that the optimal commuting operator correlation for a variant of Coladangelo's two-player generalized nonlocal game, based on the embezzlement of entanglement, is a commuting operator self-test. Our result gives the first correlation self-test for an exact entanglement embezzlement protocol in the commuting operator framework. Because the unique optimal correlation necessitates the exact embezzlement of entanglement, the correlation is unrealizable using quantum tensor-product models, even if the local spaces are allowed to be infinite dimensional. As such, our result provides an example of a commuting operator self-test where the Hilbert space shared by the two parties cannot be factored into a tensor-product of local spaces that is compatible with the local measurement operators. Our main proof technique relies on Harris' unique abstract state characterization of exact embezzlement of entanglement involving Cuntz algebras.
ER -