Non-Gaussianity bounded uncertainty relation for mixed states

Details Non-Gaussianity bounded uncertainty relation for mixed states Non-Gaussianity bounded uncertainty relation for mixed states

2009-10-19

arxiv.org/abs/0910.3473v2

Physics

Quantum Physics

12 pages, 5 figures. New version including non-Gaussianity bounded uncertainty relation for pure states (Sec. III B)

Scientific paper

We derive new uncertainty relation for one-dimensional mixed state given its purity and degree of non-Gaussianity. This relation extends the purity-bounded uncertainty relation for mixed states derived by V. V. Dodonov and V. I. Man'ko. For the special case of pure states it provides us with an extended version of the Robertson-Schrodinger uncertainty relation, saturated by a set of states which includes all the eigenstates of the quantum harmonic oscillator. We represent our results as a bound in a three-dimensional parametric space of mixed states and identify the regions of the bound realized by states with non-negative Wigner function. This takes us closer to a proper extension of Hudson's theorem to mixed states and permits us to visualize and compare the set of states with non-negative Wigner function and the set of states which minimize the newly derived uncertainty relation.

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