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 $\vert+\rangle$ 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.

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2610.06840 [quant-ph]

(or arXiv:2610.06840v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.06840 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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