Exponents for classical-quantum channel simulation in purified distance

Aadil Oufkir; Yongsheng Yao; Mario Berta

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arXiv · 2410.10770

Exponents for classical-quantum channel simulation in purified distance

Aadil Oufkir·Yongsheng Yao·Mario Berta

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Abstract

We determine the exact error and strong converse exponent for entanglement-assisted classical-quantum channel simulation in worst case input purified distance. The error exponent is expressed as a single-letter formula optimized over sandwiched R\'enyi divergences of order $\alpha \in [1, \infty)$, notably without the need for a critical rate--a sharp contrast to the error exponent for classical-quantum channel coding. The strong converse exponent is expressed as a single-letter formula optimized over sandwiched R\'enyi divergences of order $\alpha\in [\frac{1}{2},1]$. As in the classical work [Oufkir et al., arXiv:2410.07051], we start with the goal of asymptotically expanding the meta-converse for channel simulation in the relevant regimes. However, to deal with non-commutativity issues arising from classical-quantum channels and entanglement-assistance, we critically use various properties of the quantum fidelity, additional auxiliary channel techniques, approximations via Chebyshev inequalities, and entropic continuity bounds.

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Aadil Oufkir, Yongsheng Yao, Mario Berta. 2024-10-14. Exponents for classical-quantum channel simulation in purified distance. https://arxiv.org/abs/2410.10770

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