A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding
Year: 2026
Type: preprint
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 $\vert+\rangle$ and $\vert-\rangle$. 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.
Source: arXiv (Cornell University)
Authors: Havas, Tam{á}s, Lin, Hsuan-Yin, Rosnes, Eirik
Institutions: Simula UiB, University of Bergen
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220650557