Destroying and Preserving Measurement Incompatibility over a Quantum Channel
Abstract
A quantum channel is called incompatibility-breaking if it always destroys the incompatibility of quantum measurements. On the other extreme are incompatibility-preserving channels, which never destroy incompatibility. This work studies both types of channels through the mathematical framework of zonotopes and zonoids, an approach that provides a complete characterization of compatibility for dichotomic measurements and is particularly powerful in the qubit setting. Using the language of zonoids, we present necessary and sufficient conditions for when a qubit unital channel is incompatibility-breaking, which are also sufficient for nonunital channels. As one of our main results, we demonstrate the superactivation phenomenon of two incompatibility-breaking qubit channels that are no longer incompatibility-breaking when used in parallel. Translating this result into the task of quantum steering, it says that two copies of a two-qubit Werner state can be steered at noise threshold 1/2, even though this is impossible using just one copy. For the problem of incompatibility preservation, we prove that a quantum channel with matching input and output dimensions will preserve general incompatibility if and only if it is a unitary transformation. When the output dimension is larger, this result no longer holds, and we offer a conjectured form of a general incompatibility-preserving channel.
Related
- Measurement incompatibility in Bayesian quantum estimation beyond quadratic loss
- Measurement incompatibility and noiseless quantum codes
- Preservability of Measurement Incompatibility: Purification, Activation, and a No-Go Theorem
- Margenau-Hill distribution as a Necessary and Sufficient Signature of Measurement Incompatibility
- Certifying Measurement Incompatibility under Bounded Classical Communication
BibTeX
@misc{chitambar2026destroying,
title = {{Destroying and Preserving Measurement Incompatibility over a Quantum Channel}},
author = {Eric Chitambar and Yujie Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06642},
eprint = {2610.06642},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06642},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Destroying and Preserving Measurement Incompatibility over a Quantum Channel
AU - Eric Chitambar
AU - Yujie Zhang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06642
UR - https://arxiv.org/abs/2610.06642
AB - A quantum channel is called incompatibility-breaking if it always destroys the incompatibility of quantum measurements. On the other extreme are incompatibility-preserving channels, which never destroy incompatibility. This work studies both types of channels through the mathematical framework of zonotopes and zonoids, an approach that provides a complete characterization of compatibility for dichotomic measurements and is particularly powerful in the qubit setting. Using the language of zonoids, we present necessary and sufficient conditions for when a qubit unital channel is incompatibility-breaking, which are also sufficient for nonunital channels. As one of our main results, we demonstrate the superactivation phenomenon of two incompatibility-breaking qubit channels that are no longer incompatibility-breaking when used in parallel. Translating this result into the task of quantum steering, it says that two copies of a two-qubit Werner state can be steered at noise threshold 1/2, even though this is impossible using just one copy. For the problem of incompatibility preservation, we prove that a quantum channel with matching input and output dimensions will preserve general incompatibility if and only if it is a unitary transformation. When the output dimension is larger, this result no longer holds, and we offer a conjectured form of a general incompatibility-preserving channel.
ER -