Experimental Verification Of Stonger Heisenburg Uncertainty Relations

Quantum information science,as a new interdisciplinary subject,has received extensive attention and vigorous development in the past 30 years.Quantum mechanics is the physical basis of quantum information.There are many significant differences between quantum mechanics and classical theory.Quantum uncertainty relation,as an important part of quantum theory,has a profound application in quantum technology,such as quantum encryption,quantum entanglement,quantum computation and so on.The research content of this paper mainly embodies in the following two aspects:Firstly,the experimental verification is carried out for the uncertainty relationship of multiple observables based on the sum of variances.In quantum mechanics,besides a pair of conjugate observable quantities such as coordinates and momentums,there are many observables such as spin and angular momentums.We use the experimental system of linear optics to validate the more closely related uncertainty relations proposed recently in theory,and compare them with the previous inequalities.We choose the angular momentum components of the spin-1 particle in three directions as the observables.The experimental system is a threelevel quantum state.The expected value and variance of the observable are obtained by projection measurement.The experimental results are in good agreement with the theory,which further reflects the advantage of the new uncertainty relations of sum of variance.Secondly,a series of new uncertainty relations about the two observables are compared and analyzed through experiments,including the product of variance and the sum of variance.The incompatibility reflected by these new inequalities is not expressed by the commutative relation,but by the non-orthogonality between the system state and the eigenstate of the observable.By comparing these new uncertainty relations,we can find that these new uncertainty relations show a closer lower bound.In addition,we use the experimental data to discuss the inverse uncertainty relations first proposed in theory,which shows that the sum of variances or the product of variances of observables have a certain range,which is of great significance to quantum metrology.