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Main Authors: Li, Zhaoyi, Theil, Elias, Harrow, Aram W., Chuang, Isaac
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.21457
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author Li, Zhaoyi
Theil, Elias
Harrow, Aram W.
Chuang, Isaac
author_facet Li, Zhaoyi
Theil, Elias
Harrow, Aram W.
Chuang, Isaac
contents Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA), mixed-state approximate purification or cloning, and density matrix exponentiation. We show that such protocols can achieve exponentially lower sample complexity than incoherent, measurement-mediated protocols. For QPA with principal eigenstate targets and $d$-dimensional inputs, coherent processing achieves error $\varepsilon$ using $O(1/\varepsilon)$ copies, versus the $Ω(d/\varepsilon)$ copies required by any incoherent protocol. Together, these sharp coherent-incoherent separations seed a theory of coherent quantum inference, with an entanglement-breaking limit identifying the optimal incoherent counterpart of each coherent protocol.
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publishDate 2026
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spellingShingle An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
Li, Zhaoyi
Theil, Elias
Harrow, Aram W.
Chuang, Isaac
Quantum Physics
Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA), mixed-state approximate purification or cloning, and density matrix exponentiation. We show that such protocols can achieve exponentially lower sample complexity than incoherent, measurement-mediated protocols. For QPA with principal eigenstate targets and $d$-dimensional inputs, coherent processing achieves error $\varepsilon$ using $O(1/\varepsilon)$ copies, versus the $Ω(d/\varepsilon)$ copies required by any incoherent protocol. Together, these sharp coherent-incoherent separations seed a theory of coherent quantum inference, with an entanglement-breaking limit identifying the optimal incoherent counterpart of each coherent protocol.
title An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
topic Quantum Physics
url https://arxiv.org/abs/2605.21457