Lower Bounds on Error Exponents via a New Quantum Decoder

• URL: http://arxiv.org/abs/2310.09014v2
• Date: Wed, 15 Nov 2023 10:50:03 GMT
• Title: Lower Bounds on Error Exponents via a New Quantum Decoder
• Authors: Salman Beigi and Marco Tomamichel
• Abstract summary: We show new lower bounds on the error exponent on 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 bounds) channel R'enyi mutual information of order between 1/2 and 1.
• Score: 14.304623719903972
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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