Exponents for classical-quantum channel simulation in purified distance

• URL: http://arxiv.org/abs/2410.10770v1
• Date: Mon, 14 Oct 2024 17:45:41 GMT
• Title: Exponents for classical-quantum channel simulation in purified distance
• Authors: Aadil Oufkir, Yongsheng Yao, Mario Berta,
• Abstract summary: We determine the exact error and strong converse exponent for entanglement-assisted classical-quantum channel simulation. We critically use various properties of the quantum fidelity, additional auxiliary channel techniques, approximations via Chebyshev inequalities, and entropic continuity bounds.
• Score: 5.598487000369366
• License: http://creativecommons.org/licenses/by/4.0/
• 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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