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arXiv · 1504.05725

The role of quantum non-Gaussian distance in entropic uncertainty relation

Wonmin Son
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Abstract

Gaussian distribution of a quantum state with continuous spectrum is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $\hat x$ and $\hat p$, quantum entropic uncertainty relation can take a suggestive form, where the standard deviations $σ_x$ and $σ_p$ are featured explicitly. From the construction, it follows in a transparent manner that: (i) the entropic uncertainty relation implies the Kennard-Robertson uncertainty relation in a modifed form, $σ_xσ_p\geq\hbar e^{\cal N}/2$; (ii) the additional factor ${\cal N}$ quantifies the quantum non-Gaussianity of the probability distributions of two observables; (iii) the lower bound of the entropic uncertainty relation for non-gaussian continuous variable (CV) mixed state becomes stronger with purity. Optimality of specific non-gaussian CV states to the refined uncertainty relation has been investigated and the existance of new class of CV quantum state is identified.

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Wonmin Son. 2015-04-22. The role of quantum non-Gaussian distance in entropic uncertainty relation. https://doi.org/10.1103/physreva.92.012114

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