Experimental investigation of linear-entropy-based uncertainty relations in all-optical systems

Abstract

We report an all-optical experiment to investigate the uncertainty relations based on linear entropy. First we prepare two kinds of biphoton states initially, i.e., Bell-like states and Werner states. Then we perform projective measurements on one subsystem over a complete or incomplete set of mutually unbiased bases; the corresponding measurement probabilities can be directly determined by the photon coincidence counting. Together with the initial state and the postmeasurement states of the system available by quantum state tomography, linear-entropy-based uncertainty relations can be fully verified. It is shown that the experimental results agree very well with the theoretical predictions. Also, it is revealed that entanglement of the initial biphoton states is anticorrelated with the total of uncertainties. Our experimental results could not only deepen the understanding of uncertainty relations, but also facilitate potential applications to quantum technologies.