Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement

Heisenberg's uncertainty principle(1) provides a fundamental limitation on the ability of an observer holding classical information to predict the outcome when one of two measurements is performed on a quantum system. However, an observer with access to a particle (stored in a quantum memory) which is entangled with the system generally has a reduced uncertainty: indeed, if the particle and system are maximally entangled, the observer can perfectly predict the outcome of whichever measurement is chosen. This effect has recently been quantified(2) in a new entropic uncertainty relation. Here we experimentally investigate this relation, showing its effectiveness as an efficient entanglement witness. We use entangled photon pairs, an optical delay line serving as a simple quantum memory and fast, active feed-forward. Our results quantitatively agree with the new uncertainty relation. Our technique acts as a witness for almost all entangled states in our experiment as we obtain lower uncertainties than would be possible without the entangled particle(3-5).