A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding
Abstract
We investigate converse bounds on the average decoding error probability in finite-blocklength classical-quantum channel coding. We first present a lower bound for multiple quantum hypothesis testing in terms of pairwise trace distances and derive a corresponding fidelity bound. We then obtain a spectrum-based converse that depends only on the a priori probabilities and spectra of the states. We show that the converse bound remains tight for the quantum depolarizing channel under suitable conditions. For codes with product-state outputs, this converse takes an explicit form involving products of output-state eigenvalues. We apply it to binary codes over the quantum amplitude damping channel using the input states |+⟩ and |−⟩. For this setting, we also discuss a normal approximation to the spectrum-based converse in the large blocklength regime. In all numerical examples considered, the spectrum-based converse is tighter than the other converse bounds at low noise levels.
Related
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- The classical capacity of generalized amplitude-damping channels and its strong-converse exponent
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BibTeX
@misc{havas2026spectrumbased,
title = {{A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding}},
author = {Tamás Havas and Hsuan-Yin Lin and Eirik Rosnes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06840},
eprint = {2610.06840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06840},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding
AU - Tam{á}s Havas
AU - Hsuan-Yin Lin
AU - Eirik Rosnes
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06840
UR - https://arxiv.org/abs/2610.06840
AB - We investigate converse bounds on the average decoding error probability in finite-blocklength classical-quantum channel coding. We first present a lower bound for multiple quantum hypothesis testing in terms of pairwise trace distances and derive a corresponding fidelity bound. We then obtain a spectrum-based converse that depends only on the a priori probabilities and spectra of the states. We show that the converse bound remains tight for the quantum depolarizing channel under suitable conditions. For codes with product-state outputs, this converse takes an explicit form involving products of output-state eigenvalues. We apply it to binary codes over the quantum amplitude damping channel using the input states |+⟩ and |−⟩. For this setting, we also discuss a normal approximation to the spectrum-based converse in the large blocklength regime. In all numerical examples considered, the spectrum-based converse is tighter than the other converse bounds at low noise levels.
ER -