Year: 2026
Type: preprint
Abstract: One-shot information theory measures often require an optimization over states, but the form of these optimizers can be complicated or depend on the initial problem in nonlinear ways. In this note, we show that in many instances using the marginal instead of the optimal state is sufficiently good and only changes the result by a small factor. We prove that for the Petz--Rényi and sandwiched--Rényi divergences of order $α\in(0,1)$, replacing the optimizing state on $B$ by the marginal $ρ_B$ results in a multiplicative overhead of at most $1/α$.
Source: arXiv (Cornell University)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211978769