Quantum incapacity from observable shadows
Abstract
Quantum communication is ruled out when an eavesdropper can reconstruct the receiver's state. Yet states are operationally specified by measurement statistics, raising a sharper question: can access to every expectation value destroy communication? We show that it can. We call unbiased, variance-nonincreasing reconstruction under arbitrary reference extensions \emph{complete observable shadowing} and prove that it forces unassisted private and quantum capacities to vanish. An explicit qutrit channel realizes this mechanism while being neither antidegradable nor PPT, resolving the long-standing questions of whether quantum capacity can vanish outside those two classes and whether antidegradability is the only route to zero private capacity. Notably, it superactivates every finite-dimensional channel with zero quantum but positive private capacity. Statistical access can therefore preclude standalone communication without erasing latent coherent utility.
Related
- Quantum-enhanced metrology with classical shadows
- Naked Singularities and Black Hole Thermodynamics from Shadows and Photon Rings in the Quantum Oppenheimer-Snyder Model
- Federated Unlearning of Quantum Data via Classical Shadows
- Dynamic Observable Subspaces: Fast Simulation of Observable Quantum Dynamics
- The parliament of observers - Against the observable axiom of quantum mechanics
BibTeX
@misc{zhu2026quantum,
title = {{Quantum incapacity from observable shadows}},
author = {Chengkai Zhu and Xin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.24693},
eprint = {2607.24693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24693},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum incapacity from observable shadows
AU - Chengkai Zhu
AU - Xin Wang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2607.24693
UR - https://arxiv.org/abs/2607.24693
AB - Quantum communication is ruled out when an eavesdropper can reconstruct the receiver's state. Yet states are operationally specified by measurement statistics, raising a sharper question: can access to every expectation value destroy communication? We show that it can. We call unbiased, variance-nonincreasing reconstruction under arbitrary reference extensions \emph{complete observable shadowing} and prove that it forces unassisted private and quantum capacities to vanish. An explicit qutrit channel realizes this mechanism while being neither antidegradable nor PPT, resolving the long-standing questions of whether quantum capacity can vanish outside those two classes and whether antidegradability is the only route to zero private capacity. Notably, it superactivates every finite-dimensional channel with zero quantum but positive private capacity. Statistical access can therefore preclude standalone communication without erasing latent coherent utility.
ER -