Experimental test of uncertainty relations for general unitary operators

Lei Xiao, Kunkun Wang, Xiang Zhan, Zhihao Bian, Jian Li, Yongsheng Zhang, Peng Xue, and Arun Kumar Pati

Index: 10.1364/OE.25.017904

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Abstract

Uncertainty relations are the hallmarks of quantum physics and have been widely investigated since its original formulation. To understand and quantitatively capture the essence of preparation uncertainty in quantum interference, the uncertainty relations for unitary operators need to be investigated. Here, we report the first experimental investigation of the uncertainty relations for general unitary operators. In particular, we experimentally demonstrate the uncertainty relation for general unitary operators proved by Bagchi and Pati [ Phys. Rev. A 94, 042104 (2016)], which places a non-trivial lower bound on the sum of uncertainties and removes the triviality problem faced by the product of the uncertainties. The experimental findings agree with the predictions of quantum theory and respect the new uncertainty relation.