Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs

• URL: http://arxiv.org/abs/2605.21570v1
• Date: Wed, 20 May 2026 17:47:32 GMT
• Title: Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs
• Abstract summary: Quantum purity (QPA) is the task of coherently transforming $n$ copies of a mixed state into high-fidelity copies of a chosen eigenstate.<n>We characterize the optimal channel and derive its all-site and one-site performance laws across output regimes.
• Score: 5.480908143128776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 solve QPA in the general setting of $n$ input copies, $m$ output copies, arbitrary target eigenstates, arbitrary local dimension $d$, and generic input spectra. We characterize the optimal channel and derive its all-site and one-site performance laws across output regimes. For the asymptotic analysis, we use a path-graph parametrization to show that, when the target eigenvalue has a constant spectral gap $D_{k,\mathrm{min}}$, achieving all-site error $\varepsilon$ requires a number of input copies independent of $d$ and scaling as $O(m/(\varepsilon D_{k,\mathrm{min}}^2))$. 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 dimension-uniform guarantee for optimal QPA. We also provide asymptotically efficient implementations of the optimal 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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