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Joint measurability of coplanar POVMs
Abstract
An unbiased qubit positive operator-valued measure (POVM) can be uniquely expressed in terms of the Bloch vector. We prove that for POVMs with coplanar Bloch vectors, they are jointly measurable if and only if the perimeter of the convex closure of Bloch vectors is less than or equal to 4. Moreover, as a corollary, we give an affirmative answer to the conjecture suggested by [Andrejic-Kunjwal 2020] on the existence of a joint device for POVMs whose Bloch vectors lie on the same circle.
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BibTeX
@misc{yoshino2026joint,
title = {{Joint measurability of coplanar POVMs}},
author = {Taro Yoshino and Koichi Tojo and Kei Hagihara and Akinori Tanaka and Takuki Tomita},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38836},
eprint = {2609.38836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38836},
}
RIS
TY - UNPB
TI - Joint measurability of coplanar POVMs
AU - Taro Yoshino
AU - Koichi Tojo
AU - Kei Hagihara
AU - Akinori Tanaka
AU - Takuki Tomita
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38836
UR - https://arxiv.org/abs/2609.38836
AB - An unbiased qubit positive operator-valued measure (POVM) can be uniquely expressed in terms of the Bloch vector. We prove that for POVMs with coplanar Bloch vectors, they are jointly measurable if and only if the perimeter of the convex closure of Bloch vectors is less than or equal to 4. Moreover, as a corollary, we give an affirmative answer to the conjecture suggested by [Andrejic-Kunjwal 2020] on the existence of a joint device for POVMs whose Bloch vectors lie on the same circle.
ER -