Compatibility of quantum instruments
Abstract
Measurement compatibility asks whether a family of quantum measurements can be simulated by one parent measurement followed by classical post-processing. We extend this measurement compatibility to the notion of \emph{d-compatibility} for measurements, channels, and instruments whose parent passes a d-dimensional quantum system and unlimited classical information to the post-processing. We formulate d-compatibility as a common linear factorization of operator spaces and operator systems and show that d-compatible families form a closed set, even with infinitely many settings and a separable infinite-dimensional input. To certify d-incompatibility, we define the compatibility functional as the smallest product of completely bounded norms over common factorizations through a d-dimensional register. Using factorization theory of operator spaces, we show that measure-and-prepare channels defined in terms of mutually unbiased bases and pinching channels defined in terms of Heisenberg-Weyl operators are d-incompatible in certain regimes of d. We also link d-compatibility of multi-instruments to the preparability of Choi assemblages using channel-state duality, and use this connection to show that for bipartite states the (in)compatibility of instruments can be used to certify Schmidt numbers and the implementability of the instrument using one-way LOCC protocols. Finally, our compatibility functional also bounds the generalized robustness of compatibility, which we interpret through a memory-bounded nontransient preparation game.
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BibTeX
@misc{kim2026compatibility,
title = {{Compatibility of quantum instruments}},
author = {Chloe Kim and Yujie Zhang and Eric Chitambar and Marius Junge and Felix Leditzky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40266},
eprint = {2609.40266},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40266},
}
RIS
TY - UNPB
TI - Compatibility of quantum instruments
AU - Chloe Kim
AU - Yujie Zhang
AU - Eric Chitambar
AU - Marius Junge
AU - Felix Leditzky
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.40266
UR - https://arxiv.org/abs/2609.40266
AB - Measurement compatibility asks whether a family of quantum measurements can be simulated by one parent measurement followed by classical post-processing. We extend this measurement compatibility to the notion of \emph{d-compatibility} for measurements, channels, and instruments whose parent passes a d-dimensional quantum system and unlimited classical information to the post-processing. We formulate d-compatibility as a common linear factorization of operator spaces and operator systems and show that d-compatible families form a closed set, even with infinitely many settings and a separable infinite-dimensional input. To certify d-incompatibility, we define the compatibility functional as the smallest product of completely bounded norms over common factorizations through a d-dimensional register. Using factorization theory of operator spaces, we show that measure-and-prepare channels defined in terms of mutually unbiased bases and pinching channels defined in terms of Heisenberg-Weyl operators are d-incompatible in certain regimes of d. We also link d-compatibility of multi-instruments to the preparability of Choi assemblages using channel-state duality, and use this connection to show that for bipartite states the (in)compatibility of instruments can be used to certify Schmidt numbers and the implementability of the instrument using one-way LOCC protocols. Finally, our compatibility functional also bounds the generalized robustness of compatibility, which we interpret through a memory-bounded nontransient preparation game.
ER -