An uncertainty principle for unimodular quantum groups
- School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 (Canada)
We present a generalization of Hirschman's entropic uncertainty principle for locally compact Abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to q-traces of discrete quantum groups, the relative entropy with respect to the Haar weight reduces to the canonical entropy of the random walk generated by the state.
- OSTI ID:
- 22306077
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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