Certifying Measurement Incompatibility under Bounded Classical Communication
Abstract
Measurement incompatibility enables quantum advantages in communication and state discrimination. It is also necessary for Bell nonlocality, which is used in device-independent protocols for quantum key distribution and private randomness generation. Classical communication can influence the receiver's outcome and must therefore be accounted for when certifying measurement incompatibility. We introduce union maximal leakage, which quantifies the information needed for a common classical explanation of all observed probabilities and is computed from them by a linear program. If a message of at most k bits precedes the receiver's independent measurement choice, compatible measurements for each message give union maximal leakage at most k. This bound holds with any input-independent nonsignalling shared resource. In quantum theory, a violation also implies that the initially shared state is entangled. Conversely, union maximal leakage determines the minimum classical communication needed to reproduce the observations with compatible measurements and arbitrary nonsignalling assistance. For a fixed shared quantum state and receiver measurements, a violation is possible exactly when, for some message value, the receiver's measurements are Bell-nonlocal against two-outcome sender measurements on that state. For binary receiver outcomes, we show that a violation also certifies randomness private from the sender, even when the receiver's measurement depends on the sender's message and the sender retains quantum side information. We quantify this privacy through an explicit conditional entropy bound and establish composably secure randomness extraction in sequential protocols with device memory.
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
- Destroying and Preserving Measurement Incompatibility over a Quantum Channel
BibTeX
@misc{shaya2026certifying,
title = {{Certifying Measurement Incompatibility under Bounded Classical Communication}},
author = {Oxana Shaya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06722},
eprint = {2610.06722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06722},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Certifying Measurement Incompatibility under Bounded Classical Communication
AU - Oxana Shaya
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06722
UR - https://arxiv.org/abs/2610.06722
AB - Measurement incompatibility enables quantum advantages in communication and state discrimination. It is also necessary for Bell nonlocality, which is used in device-independent protocols for quantum key distribution and private randomness generation. Classical communication can influence the receiver's outcome and must therefore be accounted for when certifying measurement incompatibility. We introduce union maximal leakage, which quantifies the information needed for a common classical explanation of all observed probabilities and is computed from them by a linear program. If a message of at most k bits precedes the receiver's independent measurement choice, compatible measurements for each message give union maximal leakage at most k. This bound holds with any input-independent nonsignalling shared resource. In quantum theory, a violation also implies that the initially shared state is entangled. Conversely, union maximal leakage determines the minimum classical communication needed to reproduce the observations with compatible measurements and arbitrary nonsignalling assistance. For a fixed shared quantum state and receiver measurements, a violation is possible exactly when, for some message value, the receiver's measurements are Bell-nonlocal against two-outcome sender measurements on that state. For binary receiver outcomes, we show that a violation also certifies randomness private from the sender, even when the receiver's measurement depends on the sender's message and the sender retains quantum side information. We quantify this privacy through an explicit conditional entropy bound and establish composably secure randomness extraction in sequential protocols with device memory.
ER -