Pairwise detection, chiral conversion: Resource theory of quantum multistates
Abstract
Basis-independent coherence of a quantum multistate is fixed by whether its constituent states commute, and for qubits it is detected by pairwise state overlaps alone. What governs its deterministic transformation has been open. We give the exact resource-conversion theory of quantum multistates under common commutativity-preserving operations (CPOs). For qubits, pairwise Bargmann invariants determine the singular values of the unique candidate channel, while a single third-order Bargmann phase determines its orientation. Complete positivity then yields a necessary and sufficient criterion for exact conversion. The criterion identifies a chirality-sensitive shell ๐chir, within which targets with identical pairwise geometry can differ in convertibility solely by the sign of their cubic invariant. This yields an order separation, kdetect=2<3=kconvert, for qubit multistates of every size ngeqslant3. The chirality-sensitive shell occupies exactly one third of the singular-value simplex, while mirror reflection obstructs two thirds of the admissible orientation-preserving transformations by volume. For dgeqslant3, by contrast, the structure is rigid: every resourceful conversion is realized by either an isotropic depolarizing or a transpose-depolarizing channel. Convertibility is then decided by centered Bargmann invariants of degree at most d2.
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BibTeX
@misc{tao2026pairwise,
title = {{Pairwise detection, chiral conversion: Resource theory of quantum multistates}},
author = {Yuan-Hong Tao and Yu-Xin Wu and Bing Xie and Lin Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04930},
eprint = {2610.04930},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04930},
}
RIS
TY - UNPB
TI - Pairwise detection, chiral conversion: Resource theory of quantum multistates
AU - Yuan-Hong Tao
AU - Yu-Xin Wu
AU - Bing Xie
AU - Lin Zhang
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04930
UR - https://arxiv.org/abs/2610.04930
AB - Basis-independent coherence of a quantum multistate is fixed by whether its constituent states commute, and for qubits it is detected by pairwise state overlaps alone. What governs its deterministic transformation has been open. We give the exact resource-conversion theory of quantum multistates under common commutativity-preserving operations (CPOs). For qubits, pairwise Bargmann invariants determine the singular values of the unique candidate channel, while a single third-order Bargmann phase determines its orientation. Complete positivity then yields a necessary and sufficient criterion for exact conversion. The criterion identifies a chirality-sensitive shell ๐_chir, within which targets with identical pairwise geometry can differ in convertibility solely by the sign of their cubic invariant. This yields an order separation, k_detect=2<3=k_convert, for qubit multistates of every size ngeqslant3. The chirality-sensitive shell occupies exactly one third of the singular-value simplex, while mirror reflection obstructs two thirds of the admissible orientation-preserving transformations by volume. For dgeqslant3, by contrast, the structure is rigid: every resourceful conversion is realized by either an isotropic depolarizing or a transpose-depolarizing channel. Convertibility is then decided by centered Bargmann invariants of degree at most d^2.
ER -