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Quantum Information Processing

Quantitative wave–particle duality relations from the density matrix properties

  • 01-08-2020
Published in:
Authors
Marcos L. W. Basso
Diego S. S. Chrysosthemos
Jonas Maziero
Published in
Quantum Information Processing | Issue 8/2020

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Abstract

We derive upper bounds for Hilbert–Schmidt’s quantum coherence of general states of a d-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 \(l_{1}\)-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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previous article Multi-user quantum private query
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Title
Quantitative wave–particle duality relations from the density matrix properties
Authors
Marcos L. W. Basso
Diego S. S. Chrysosthemos
Jonas Maziero
Publication date
01-08-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 8/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02753-y
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