Asymptotically Optimal Mixed-State Cloning
Abstract
We determine asymptotic global fidelities of cloning generic mixed states with simple (non-degenerate) full-rank spectra. In fixed dimension d, let n inputs and mn outputs satisfy mn/n→γ>1. For a known simple full-rank spectrum p1>⋯>pd>0, we prove that the optimal root fidelity between the entire output and the product target state is Forb(γ,p) =∏i<j (√γ+√(qij(γ−1+qij)))/(γ+qij), qij=pj/pi. When the spectrum is unknown, one spectrum-independent cloner attains Funiv(γ,p) =(2√γ/(1+γ))(d−1)/2 Forb(γ,p), uniformly on compact subsets of the simple full-rank chamber and is minimax optimal. The two factors quantify spectral and eigenbasis uncertainty. Our channels combine classical processing of Schur--Weyl labels with a covariant Cartan-sector channel. Local asymptotic normality and a Gaussian fidelity bound against arbitrary channels yield the converses. For flat projector states ρ=P/r, with P a rank-r orthogonal projector, we separately prove the optimum γ−r(d−r)/2. Furthermore, we estimate the exact asymptotic fidelity of purify--clone--trace (PCT), and show that our cloners strictly outperform PCT at every fixed gain for simple full-rank spectra and rank-r projector states with 1<r<d.
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BibTeX
@misc{fei2026asymptotically,
title = {{Asymptotically Optimal Mixed-State Cloning}},
author = {Jiani Fei and Jinzhao Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35986},
eprint = {2609.35986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35986},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Asymptotically Optimal Mixed-State Cloning
AU - Jiani Fei
AU - Jinzhao Wang
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35986
UR - https://arxiv.org/abs/2609.35986
AB - We determine asymptotic global fidelities of cloning generic mixed states with simple (non-degenerate) full-rank spectra. In fixed dimension d, let n inputs and m_n outputs satisfy m_n/n→γ>1. For a known simple full-rank spectrum p_1>⋯>p_d>0, we prove that the optimal root fidelity between the entire output and the product target state is F_orb(γ,p) =∏_i<j (√γ+√(q_ij(γ−1+q_ij)))/(γ+q_ij), q_ij=p_j/p_i. When the spectrum is unknown, one spectrum-independent cloner attains F_univ(γ,p) =(2√γ/(1+γ))^(d−1)/2 F_orb(γ,p), uniformly on compact subsets of the simple full-rank chamber and is minimax optimal. The two factors quantify spectral and eigenbasis uncertainty. Our channels combine classical processing of Schur--Weyl labels with a covariant Cartan-sector channel. Local asymptotic normality and a Gaussian fidelity bound against arbitrary channels yield the converses. For flat projector states ρ=P/r, with P a rank-r orthogonal projector, we separately prove the optimum γ^−r(d−r)/2. Furthermore, we estimate the exact asymptotic fidelity of purify--clone--trace (PCT), and show that our cloners strictly outperform PCT at every fixed gain for simple full-rank spectra and rank-r projector states with 1<r<d.
ER -