  We propose a trade-off between the Lipschitz constants of the position and
momentum probability distributions for arbitrary quantum states. We refer to
the trade-off as a quantum reciprocity relation. The Lipschitz constant of a
function may be considered to quantify the extent of fluctuations of that
function, and is, in general, independent of its spread. The spreads of the
position and momentum distributions are used to obtain the celebrated
Heisenberg quantum uncertainty relations. We find that the product of the
Lipschitz constants of position and momentum probability distributions is
bounded below by a number that is of the order of the inverse square of the
Planck's constant.
