Quantum coherence as randomness under classical control
Abstract
Quantum states that do not commute exhibit coherence, but only when the device preparing them is assumed to be unaffected by classical parameters inaccessible to the experimenter. Accounting for such hidden classical control leads to a stronger notion of coherence. We establish its significance through the task of randomness certification. It is shown that a preparation device is coherent if and only if it can be used to certify randomness in a prepare-and-measure experiment. This operational interpretation motivates the problem of certifying coherence in the presence of hidden classical control. We obtain a complete characterisation of coherence through a hierarchy of semidefinite programs. Then, we introduce a practical semidefinite programming approach that achieves useful accuracy while remaining computationally efficient even for devices preparing many, potentially high-dimensional, quantum states. For the important case of qubits, we further exploit connections with the theory of joint measurability to obtain highly accurate coherence characterisation that scales to more than one thousand qubit states. Our results give operational meaning to quantum coherence under hidden classical control and provide a versatile toolbox for its certification.
Related
- Induced Coherence in Quantum and Classical Interferometry: Origin and Control
- Classical Verification of a Remote Quantum Processor via Degenerate Concordant Computations: An Application to Randomness Generation
- Disorder-driven loss of crystalline coherence in two-dimensional electron solids: Quantum Hartree-Fock and classical molecular dynamics
- Classical Reversible Computation by Quantum Coherence
- Where to Decide: Control-Plane Geometry in Coherence-Limited Quantum Networks
BibTeX
@misc{cobucci2026quantum,
title = {{Quantum coherence as randomness under classical control}},
author = {Gabriele Cobucci and Nicola D'Alessandro and Raphael Brinster and Alexander Bernal and Nikolai Wyderka and Armin Tavakoli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.03699},
eprint = {2606.03699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03699},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum coherence as randomness under classical control
AU - Gabriele Cobucci
AU - Nicola D'Alessandro
AU - Raphael Brinster
AU - Alexander Bernal
AU - Nikolai Wyderka
AU - Armin Tavakoli
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.03699
UR - https://arxiv.org/abs/2606.03699
AB - Quantum states that do not commute exhibit coherence, but only when the device preparing them is assumed to be unaffected by classical parameters inaccessible to the experimenter. Accounting for such hidden classical control leads to a stronger notion of coherence. We establish its significance through the task of randomness certification. It is shown that a preparation device is coherent if and only if it can be used to certify randomness in a prepare-and-measure experiment. This operational interpretation motivates the problem of certifying coherence in the presence of hidden classical control. We obtain a complete characterisation of coherence through a hierarchy of semidefinite programs. Then, we introduce a practical semidefinite programming approach that achieves useful accuracy while remaining computationally efficient even for devices preparing many, potentially high-dimensional, quantum states. For the important case of qubits, we further exploit connections with the theory of joint measurability to obtain highly accurate coherence characterisation that scales to more than one thousand qubit states. Our results give operational meaning to quantum coherence under hidden classical control and provide a versatile toolbox for its certification.
ER -