Quantitative wave-particle duality relations from the density matrix properties
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Publication:6306847
DOI10.1007/S11128-020-02753-YarXiv1809.06354MaRDI QIDQ6306847
Diego S. S. Chrysosthemos, Marcos L. W. Basso, Jonas Maziero
Publication date: 17 September 2018
Abstract: We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a -level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the corresponding closest incoherent state. Similar bounds are obtained for Wigner-Yanase's coherence. The reported inequalities are also given as coherence-populations trade-off relations. As an application example of these inequalities, we derive quantitative wave-particle duality relations for multi-slit interferometry. Our framework leads to the identification of predictability measures complementary to Hilbert-Schmidt's, Wigner-Yanase's, and -norm quantum coherences. The quantifiers reported here for the wave and particle aspects of a quanton follow directly from the defining properties of the quantum density matrix (i.e., semi-positivity and unit trace), contrasting thus with most related results from the literature.
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