An Exponential Sample-Complexity Advantage for Coherent Quantum Inference

@misc{li2026exponential,
  title = {{An Exponential Sample-Complexity Advantage for Coherent Quantum Inference}},
  author = {Zhaoyi Li and Elias Theil and Aram W. Harrow and Isaac Chuang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.21457},
  eprint = {2605.21457},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.21457},
}

TY  - UNPB
TI  - An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
AU  - Zhaoyi Li
AU  - Elias Theil
AU  - Aram W. Harrow
AU  - Isaac Chuang
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2605.21457
UR  - https://arxiv.org/abs/2605.21457
AB  - 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 ε using O(1/ε) copies, whereas any incoherent protocol requires Ω(d/ε) copies. Together, these separations motivate a unified picture of coherent quantum inference, in which an entanglement-breaking limit identifies the optimal incoherent counterpart.
ER  -