Entropic uncertainty relations under localizations on discrete quantum groups. (English) Zbl 1405.81055
In this paper, the author demonstrates that entropic uncertainty relations can be strengthened under localizations on discrete quantum groups. This is valid is the dual compact quantum group \(\mathbb G\) is the free orthogonal quantum group \(O^+_N\) with \(N \geqslant 3\) or if \(\mathbb G\) admits an infinite \(\Lambda (p)\) set with \(p>2\). Moreover the author shows why this cannot be done if \(\mathbb G\) is a compact connected semisimple Lie group, or \(O^+_2\), or \(\mathrm{SU}_q(2)\) with \(0 < q < 1\).
Reviewer: Nenad Manojlović (Faro)
MSC:
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 94A17 | Measures of information, entropy |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 22D25 | \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations |
| 20G42 | Quantum groups (quantized function algebras) and their representations |
| 46L05 | General theory of \(C^*\)-algebras |
| 46L52 | Noncommutative function spaces |
Keywords:
harmonic analysis; quantum mechanical entropy; topological groups; uncertainty principle; Fourier analysis; functional analysisReferences:
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