Year: 2026
Type: preprint
Abstract: We study a returning quantum change interval in which a source emits $\lvertψ\rangle$ over one interval and $\lvert0\rangle$ elsewhere. A collective measurement on the full sequence identifies both endpoints with minimum error. We analyze the Gram matrix using Toeplitz comparison and Følner transfer, together with an exact decomposition by excitation number and interval hull. The resulting bounds establish asymptotic Bayes optimality of the square root measurement (SRM). Let $c=\lvert\langle0\vertψ\rangle\rvert$ and $p_1(x)=4(1-x^2)K^2(x^2)/π^2$, where $K$ is the complete elliptic integral of the first kind. For a known interval length $i$, the SRM success probability and the Bayes optimum converge to the same Toeplitz symbol integral as the number $N$ of translations grows. For fixed $i$ and $0
Source: arXiv (Cornell University)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G4930261070
OpenAlex ID: W7204257270