Coherence and imaginarity of qubit states under vanishing Bargmann invariants
Abstract
Set coherence and set imaginarity are two important quantum resources defined by sets of states. We investigate tuples of qubit states under vanishing higher-order Bargmann invariants and show that their set coherence and set imaginarity are each related to whether they contain a pair of orthogonal states. Specifically, when the relevant higher-order Bargmann invariants vanish, the tuple contains a pair of orthogonal states if and only if removing some state makes the remaining tuple incoherent. Moreover, when maximally mixed states are excluded, the same vanishing conditions imply that the tuple is imaginarity-free if and only if it contains a pair of orthogonal states. As a consequence, under these conditions, a tuple of single-qubit states has imaginarity precisely when every tuple obtained by deleting one of its states is coherent.
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BibTeX
@misc{wang2026coherence,
title = {{Coherence and imaginarity of qubit states under vanishing Bargmann invariants}},
author = {Hao-Fan Wang and Lin Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30618},
eprint = {2610.30618},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30618},
}
RIS
TY - UNPB
TI - Coherence and imaginarity of qubit states under vanishing Bargmann invariants
AU - Hao-Fan Wang
AU - Lin Chen
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30618
UR - https://arxiv.org/abs/2610.30618
AB - Set coherence and set imaginarity are two important quantum resources defined by sets of states. We investigate tuples of qubit states under vanishing higher-order Bargmann invariants and show that their set coherence and set imaginarity are each related to whether they contain a pair of orthogonal states. Specifically, when the relevant higher-order Bargmann invariants vanish, the tuple contains a pair of orthogonal states if and only if removing some state makes the remaining tuple incoherent. Moreover, when maximally mixed states are excluded, the same vanishing conditions imply that the tuple is imaginarity-free if and only if it contains a pair of orthogonal states. As a consequence, under these conditions, a tuple of single-qubit states has imaginarity precisely when every tuple obtained by deleting one of its states is coherent.
ER -