Necessary and sufficient condition for joint measurability
Quantum Physics
2019-09-25 v1
Abstract
In order to analyze joint measurability of given measurements, we introduce a Hermitian operator-valued measure, called -measure, such that it has marginals of positive operator-valued measures (POVMs). We prove that -measure is a POVM {\em if and only if} its marginal POVMs are jointly measurable. The proof suggests to employ the negatives of -measure as an indicator for non-joint measurability. By applying triangle inequalities to the negativity, we derive joint measurability criteria for dichotomic and trichotomic variables. Also, we propose an operational test for the joint measurability in sequential measurement scenario.
Cite
@article{arxiv.1904.01785,
title = {Necessary and sufficient condition for joint measurability},
author = {Jeongwoo Jae and Kyunghyun Baek and Junghee Ryu and Jinhyoung Lee},
journal= {arXiv preprint arXiv:1904.01785},
year = {2019}
}