Preservability of Measurement Incompatibility: Purification, Activation, and a No-Go Theorem
Abstract
Measurement incompatibility is a fundamental quantum resource that enables advantages in many quantum information tasks, including cryptography and communication. However, unavoidable interactions between a system and its environment can degrade or even completely destroy measurement incompatibility; such a process is referred to as a measurement-incompatibility-annihilating channel. Recently, the capability of noisy quantum dynamics to preserve measurement incompatibility has been characterized within the resource theory of measurement incompatibility preservability. This motivates studying how to purify the preservation of measurement incompatibility and how to activate it from a measurement-incompatibility-annihilating channel. To this end, we first introduce our figures of merit as robustness-based resource monotones within this resource theory. We demonstrate that while pre-filtering operations can strengthen measurement incompatibility preservability, they cannot activate it from an incompatibility-annihilating channel, establishing a no-go theorem. Furthermore, we explicitly demonstrate that an incompatibility-annihilating channel can be stochastically activated via post-filtering operations. Our results provide a practical framework for exploiting measurement incompatibility in quantum information processing.
Related
- Measurement incompatibility in Bayesian quantum estimation beyond quadratic loss
- Measurement incompatibility and noiseless quantum codes
- Margenau-Hill distribution as a Necessary and Sufficient Signature of Measurement Incompatibility
- Destroying and Preserving Measurement Incompatibility over a Quantum Channel
- Certifying Measurement Incompatibility under Bounded Classical Communication
BibTeX
@misc{wu2026preservability,
title = {{Preservability of Measurement Incompatibility: Purification, Activation, and a No-Go Theorem}},
author = {Chao-Hsien Wu and Franco Nori and Huan-Yu Ku},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01327},
eprint = {2610.01327},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01327},
note = {CC0},
}
RIS
TY - UNPB
TI - Preservability of Measurement Incompatibility: Purification, Activation, and a No-Go Theorem
AU - Chao-Hsien Wu
AU - Franco Nori
AU - Huan-Yu Ku
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01327
UR - https://arxiv.org/abs/2610.01327
AB - Measurement incompatibility is a fundamental quantum resource that enables advantages in many quantum information tasks, including cryptography and communication. However, unavoidable interactions between a system and its environment can degrade or even completely destroy measurement incompatibility; such a process is referred to as a measurement-incompatibility-annihilating channel. Recently, the capability of noisy quantum dynamics to preserve measurement incompatibility has been characterized within the resource theory of measurement incompatibility preservability. This motivates studying how to purify the preservation of measurement incompatibility and how to activate it from a measurement-incompatibility-annihilating channel. To this end, we first introduce our figures of merit as robustness-based resource monotones within this resource theory. We demonstrate that while pre-filtering operations can strengthen measurement incompatibility preservability, they cannot activate it from an incompatibility-annihilating channel, establishing a no-go theorem. Furthermore, we explicitly demonstrate that an incompatibility-annihilating channel can be stochastically activated via post-filtering operations. Our results provide a practical framework for exploiting measurement incompatibility in quantum information processing.
ER -