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.

arXiv:2606.03699 [quant-ph]

(or arXiv:2606.03699v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.03699 Focus to learn more arXiv-issued DOI via DataCite

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