86 research outputs found
Strong Majorization Entropic Uncertainty Relations
We analyze entropic uncertainty relations in a finite dimensional Hilbert
space and derive several strong bounds for the sum of two entropies obtained in
projective measurements with respect to any two orthogonal bases. We improve
the recent bounds by Coles and Piani, which are known to be stronger than the
well known result of Maassen and Uffink. Furthermore, we find a novel bound
based on majorization techniques, which also happens to be stronger than the
recent results involving largest singular values of submatrices of the unitary
matrix connecting both bases. The first set of new bounds give better results
for unitary matrices close to the Fourier matrix, while the second one provides
a significant improvement in the opposite sectors. Some results derived admit
generalization to arbitrary mixed states, so that corresponding bounds are
increased by the von Neumann entropy of the measured state. The majorization
approach is finally extended to the case of several measurements.Comment: Revised versio
Contrast in Multipath Interference and Quantum Coherence
We develop a rigorous connection between statistical properties of an
interference pattern and the coherence properties of the underlying quantum
state. With explicit examples, we demonstrate that even for inaccurate
reconstructions of interference patterns properly defined statistical moments
permit a reliable characterization of quantum coherence.Comment: 10 page
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