Lower Bounds on Error Exponents via a New Quantum Decoder
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915411499417600 |
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| author | Beigi, Salman Tomamichel, Marco |
| author_facet | Beigi, Salman Tomamichel, Marco |
| contents | 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 Rényi 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09014 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lower Bounds on Error Exponents via a New Quantum Decoder Beigi, Salman Tomamichel, Marco Quantum Physics 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 Rényi 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. |
| title | Lower Bounds on Error Exponents via a New Quantum Decoder |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2310.09014 |