Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs
Abstract
Quantum purity amplification (QPA) is the task of coherently transforming n copies of a mixed state into high-fidelity copies of a chosen eigenstate. We develop a general theory of QPA for n input copies, m output copies, and arbitrary choices of target eigenstate, local dimension d, and input spectrum. We introduce the overhang-removal protocol, derive its all-site and one-site fidelities across output regimes, and show that it is optimal in several regimes, both asymptotically and nonasymptotically. For the asymptotic analysis, we use a path-graph parametrization to show that, when the target eigenvalue has a constant spectral gap Dk,min, achieving worst-case all-site error ε scales as O(m/(ε Dk,min2)). When m/n approaches a constant, the performance exhibits phase-like regimes, which we characterize explicitly. For the nonasymptotic analysis, we develop a theory of generalized Young diagrams that yields tight sample complexity bounds and provides the first tight dimension-uniform guarantee for optimal QPA. We also provide asymptotically efficient implementations of the overhang-removal protocol. Together, these results establish QPA as a rigorous example of coherent quantum information processing with dimension-uniform sample complexity, supplying the technical foundation for the coherent-incoherent separation developed in the companion work.
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BibTeX
@misc{li2026quantum,
title = {{Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs}},
author = {Zhaoyi Li and Elias Theil and Aram W. Harrow and Isaac Chuang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.21570},
eprint = {2605.21570},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21570},
}
RIS
TY - UNPB
TI - Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs
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.2605.21570
UR - https://arxiv.org/abs/2605.21570
AB - Quantum purity amplification (QPA) is the task of coherently transforming n copies of a mixed state into high-fidelity copies of a chosen eigenstate. We develop a general theory of QPA for n input copies, m output copies, and arbitrary choices of target eigenstate, local dimension d, and input spectrum. We introduce the overhang-removal protocol, derive its all-site and one-site fidelities across output regimes, and show that it is optimal in several regimes, both asymptotically and nonasymptotically. For the asymptotic analysis, we use a path-graph parametrization to show that, when the target eigenvalue has a constant spectral gap D_k,min, achieving worst-case all-site error ε scales as O(m/(ε D_k,min^2)). When m/n approaches a constant, the performance exhibits phase-like regimes, which we characterize explicitly. For the nonasymptotic analysis, we develop a theory of generalized Young diagrams that yields tight sample complexity bounds and provides the first tight dimension-uniform guarantee for optimal QPA. We also provide asymptotically efficient implementations of the overhang-removal protocol. Together, these results establish QPA as a rigorous example of coherent quantum information processing with dimension-uniform sample complexity, supplying the technical foundation for the coherent-incoherent separation developed in the companion work.
ER -