Asymptotic entropic uncertainty relations
| Author | Adamczak R.; Latała R.; Puchała Z.; Życzkowski K. |
|---|---|
| Title | Asymptotic entropic uncertainty relations |
| Journal | J. Math. Phys. |
| Year | 2016 |
| Status | Published |
| Volume | 57 |
| DOI | 10.1063/1.4944425 |
| URL | http://dx.doi.org/10.1063/1.4944425 |
| Abstract | <p>Entropic uncertainty relations are analyzed for the case of N-dimensional Hilbert space and two orthogonal measurements performed in two generic bases, related by a Haar random unitary matrix U. We derive estimations for the average norms of truncations of U of a given size, which allow us to study state-independent lower bounds for the sum of two entropies describing the measurements outcomes. In particular, we show that the Maassen–Uffink bound asymptotically behaves as lnN−lnlnN−ln2, while the strong entropic majorization relation yields a nearly optimal bound, lnN−const. Analogous results are also obtained for a more general case of several orthogonal measurements performed in generic bases.</p> |