An Exponential Sample-Complexity Advantage for Coherent Quantum Inference

Abstract:Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum. Such settings include quantum purity amplification (QPA), random purification and approximate cloning, and density matrix exponentiation. We show that such protocols can achieve exponentially lower sample complexity than incoherent, measurement-mediated protocols, establishing, to the best of our knowledge, the first nontrivial separations between dimension-independent coherent and dimension-dependent incoherent sample complexity. For QPA with principal-eigenstate targets and $d$-dimensional inputs, at fixed output number and spectral gap, coherent processing achieves error $\varepsilon$ using $O(1/\varepsilon)$ copies, whereas any incoherent protocol requires $\Omega(d/\varepsilon)$ copies. Together, these separations motivate a unified picture of coherent quantum inference, in which an entanglement-breaking limit identifies the optimal incoherent counterpart.

arXiv:2605.21457 [quant-ph]

(or arXiv:2605.21457v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.21457 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.