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Mathematics 2016, 4(3), 47;

Uncertainty Relations for Quantum Coherence

Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain
Author to whom correspondence should be addressed.
Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari
Received: 4 April 2016 / Revised: 8 July 2016 / Accepted: 9 July 2016 / Published: 16 July 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
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Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more noncommuting reference bases respects uncertainty like relations for a given state of single and bipartite quantum systems. In the case of bipartite systems, we find that the presence of entanglement may tighten the above relation. Further, we find an upper bound on the sum of the relative entropies of coherence of bipartite quantum states in two noncommuting reference bases. Moreover, we provide an upper bound on the absolute value of the difference of the relative entropies of coherence calculated with respect to two incompatible bases. View Full-Text
Keywords: uncertainty relations; coherence; quantum correlations uncertainty relations; coherence; quantum correlations

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Singh, U.; Pati, A.K.; Bera, M.N. Uncertainty Relations for Quantum Coherence. Mathematics 2016, 4, 47.

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