Rényi divergences and binary state discrimination error exponents for fermionic quasi-free states
Abstract
The trade-off relations between the two types of error probabilities in binary i.i.d. quantum state discrimination can be expressed by single-copy formulas in terms of the Petz-type and the sandwiched Rényi divergences of the two states representing the two hypotheses. In the non-i.i.d. setting, the error exponents can usually be expressed in terms of regularized Rényi divergences, which do not admit explicit formulas in general. Here, we consider a class of states, translation-invariant and gauge-invariant quasifree states on doubly infinite fermionic chains, and give explicit formulas for a wide range of regularized Rényi divergences between such states, including (α,z), log-Euclidean, geometric, measured, and the recently introduced integral Rényi divergences. We show that the case where there is a single mode at each lattice site becomes asymptotically classical, with all the different types of regularized Rényi divergences being equal, while in the case of multiple modes per site, non-commutativity persists under regularization, and for any fixed α, the regularized Rényi (α,z)-divergences give different regularized values for different z parameters in general. We also generalize a previous construction from [Bunth, Maróti, Mosonyi, Zimborás, Lett.~Math.~Phys.~113:(7), 2023] to the case of multiple modes per lattice site to obtain a large class of states exhibiting super-exponential decay of the discrimination error probabilities.
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BibTeX
@misc{mosonyi2026rényi,
title = {{Rényi divergences and binary state discrimination error exponents for fermionic quasi-free states}},
author = {Milán Mosonyi and Gábor Maróti-Zareczky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.31379},
eprint = {2605.31379},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.31379},
}
RIS
TY - UNPB
TI - Rényi divergences and binary state discrimination error exponents for fermionic quasi-free states
AU - Milán Mosonyi
AU - Gábor Maróti-Zareczky
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.31379
UR - https://arxiv.org/abs/2605.31379
AB - The trade-off relations between the two types of error probabilities in binary i.i.d. quantum state discrimination can be expressed by single-copy formulas in terms of the Petz-type and the sandwiched Rényi divergences of the two states representing the two hypotheses. In the non-i.i.d. setting, the error exponents can usually be expressed in terms of regularized Rényi divergences, which do not admit explicit formulas in general. Here, we consider a class of states, translation-invariant and gauge-invariant quasifree states on doubly infinite fermionic chains, and give explicit formulas for a wide range of regularized Rényi divergences between such states, including (α,z), log-Euclidean, geometric, measured, and the recently introduced integral Rényi divergences. We show that the case where there is a single mode at each lattice site becomes asymptotically classical, with all the different types of regularized Rényi divergences being equal, while in the case of multiple modes per site, non-commutativity persists under regularization, and for any fixed α, the regularized Rényi (α,z)-divergences give different regularized values for different z parameters in general. We also generalize a previous construction from [Bunth, Maróti, Mosonyi, Zimborás, Lett.~Math.~Phys.~113:(7), 2023] to the case of multiple modes per lattice site to obtain a large class of states exhibiting super-exponential decay of the discrimination error probabilities.
ER -