Imaginarity witnessing enhancement via spectral norms of witnesses
Abstract
Quantum imaginarity is an essential physical resource that underpins key functionalities of modern quantum technologies. We improve imaginarity witnessing via the prior knowledge of imaginarity-witness operators. To this end, we derive a rigorous upper bound on the maximum expectation value of an imaginarity witness operator over the set of all free (real) quantum states, which is given by the spectral norm of the real component of the corresponding witness operator. We demonstrate via detailed examples that this bound substantially improves imaginarity detection. We further classify all imaginarity-witness operators into four distinct families based on this bound. For these four witness classes, we perform a comprehensive analysis of their completeness and finite completeness, the joint detection of shared imaginary quantum states by different witnesses, and the conditions for distinct witnesses to identify identical imaginary states. Our results advance the fundamental understanding of imaginarity detection and offer useful insights for both theoretical studies and experimental implementations of quantum imaginarity.
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BibTeX
@misc{xie2026imaginarity,
title = {{Imaginarity witnessing enhancement via spectral norms of witnesses}},
author = {Yuhang Xie and Yanjun Chu and Yushan Ding and Shao-Ming Fei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00534},
eprint = {2609.00534},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00534},
}
RIS
TY - UNPB
TI - Imaginarity witnessing enhancement via spectral norms of witnesses
AU - Yuhang Xie
AU - Yanjun Chu
AU - Yushan Ding
AU - Shao-Ming Fei
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.00534
UR - https://arxiv.org/abs/2609.00534
AB - Quantum imaginarity is an essential physical resource that underpins key functionalities of modern quantum technologies. We improve imaginarity witnessing via the prior knowledge of imaginarity-witness operators. To this end, we derive a rigorous upper bound on the maximum expectation value of an imaginarity witness operator over the set of all free (real) quantum states, which is given by the spectral norm of the real component of the corresponding witness operator. We demonstrate via detailed examples that this bound substantially improves imaginarity detection. We further classify all imaginarity-witness operators into four distinct families based on this bound. For these four witness classes, we perform a comprehensive analysis of their completeness and finite completeness, the joint detection of shared imaginary quantum states by different witnesses, and the conditions for distinct witnesses to identify identical imaginary states. Our results advance the fundamental understanding of imaginarity detection and offer useful insights for both theoretical studies and experimental implementations of quantum imaginarity.
ER -