1304.4506 (T. Pramanik et al.)

Optimal lower bound of quantum uncertainty from extractable classical
information    [PDF]

T. Pramanik, S. Mal, A. S. Majumdar

The sum of entropic uncertainties for the measurement of two non-commuting observables is not always reduced by the amount of entanglement (quantum memory) between two parties, and in certain cases may be impacted by quantum correlations beyond entanglement (discord). However, in any operational situation, the optimal lower bound of entropic uncertainty is given by fine-graining. Here we derive a new uncertainty relation where the maximum possible reduction of uncertainty is shown to be given by the extractable classical information, thus providing an explanation in terms of physical resources for the operationally relevant fine-graining for determining the minimum uncertainty. We illustrate this result through examples of pure and mixed entangled states, and also separable states with non-vanishing discord. Using our uncertainty relation we further show that even in the absence of any quantum correlations between the two parties, the sum of uncertainties may be reduced with the help of classical correlations.

View original: http://arxiv.org/abs/1304.4506