Leo Bia | Searcharxiv

arXiv2026

Saturating the Bayesian Nagaoka-Hayashi bound within numerical precision for the depolarization SU(2) rotation channel

The Bayesian Nagaoka--Hayashi (NH) bound is a semidefinite lower bound on the Bayes risk of multiparameter estimation, tighter than the Bayesian symmertic logarithmic derivative (SLD) Cram\'er--Rao bounds, and whether it can be attained is an open problem. We study the single-shot estimation of a qubit rotation, all three parameters at once, under depolarizing noise and a uniform prior, with $k$ parallel uses of the channel. Rotational covariance reduces the joint optimization of probe, measurement, and estimator, and the NH bound itself, to small semidefinite programs, solvable through $k=4$. At every number of uses and noise strength the optimized strategy reaches the NH bound within the numerical precision of the calculation, numerical evidence that the bound is attained for this channel family, while the SLD bound lies strictly below and is never attained. As the noise grows the optimal probe collapses to the tensored Bell state.

quant-ph↗

arXiv2025

Bayesian Greedy Receiver for Pulse Position Modulation without an Error Floor under Thermal Noise

We investigate quantum receiver architectures for demodulation $M$-ary Pulse Position Modulation under thermal noise and photon-starved conditions. Building on the greed receiver framework, we analyze it using jointly optimized displacement-squeezing and the Dolinar receiver. We further introduce a novel slicing Bayesian greedy receiver, which partitions each PPM time slot into multiple optical slices and update the full posterior distribution over codeword hypothesis at each slice using Bayes' rule. Under the presence of noise, our slicing greedy receiver outperforms the standard greedy receiver and appears to avoid a noise floor given sufficient slicing resolution.

quant-ph↗