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- W2951246458 abstract "In certain circumstances, the uncertainty, $Delta S [phi]$, of a quantum observable, $S$, can be bounded from below by a finite overall constant $Delta S>0$, emph{i.e.}, $Delta S [phi] geq Delta S$, for all physical states $phi$. For example, a finite lower bound to the resolution of distances has been used to model a natural ultraviolet cutoff at the Planck or string scale. In general, the minimum uncertainty of an observable can depend on the expectation value, $t=langle phi, S phirangle$, through a function $Delta S_t$ of $t$, emph{i.e.}, $Delta S [phi]ge Delta S_t$, for all physical states $phi$ with $langle phi, S phirangle=t$. An observable whose uncertainty is finitely bounded from below is necessarily described by an operator that is merely symmetric rather than self-adjoint on the physical domain. Nevertheless, on larger domains, the operator possesses a family of self-adjoint extensions. Here, we prove results on the relationship between the spacing of the eigenvalues of these self-adjoint extensions and the function $Delta S_t$. We also discuss potential applications in quantum and classical information theory." @default.
- W2951246458 created "2019-06-27" @default.
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- W2951246458 date "2015-08-24" @default.
- W2951246458 modified "2023-09-23" @default.
- W2951246458 title "Quantum uncertainty and the spectra of symmetric operators" @default.
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- W2951246458 doi "https://doi.org/10.48550/arxiv.1508.05735" @default.
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