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arXiv · 2310.09014

Lower Bounds on Error Exponents via a New Quantum Decoder

Salman Beigi·Marco Tomamichel
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Abstract

We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic regimes for the classical-quantum and the entanglement-assisted channel coding problem. Our bounds are expressed in terms of measured (for the one-shot bounds) and sandwiched (for the asymptotic bounds) channel R\'enyi mutual information of order between 1/2 and 1. Our results are not comparable with some previously established bounds for general instances, yet they are tight (for rates close to capacity) when the underlying channel is classical.

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Salman Beigi, Marco Tomamichel. 2023-10-13. Lower Bounds on Error Exponents via a New Quantum Decoder. https://doi.org/10.1109/tit.2024.3446614

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