Uncertainty principle, as one of the most striking features in quantum mechanics, has many useful applications in quantum information theory, such as entanglement detection and error-disturbance relation. The corresponding uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of measurement outcomes for a pair of noncommuting observables. Although one can obtain an uncertainty relation for multiple observables by multiplying or summing over the uncertainty inequalities for all the pairs of these observables, the resulting lower bounds of such obtained uncertainty relation are generally not tight. For instance, three pairwise canonical observables p（momentum），q（position），r=-p-q are considered in combination with Heisenberg-Robertson uncertainty relation. However, by introducing the triple constant

a tight triple uncertainty relation in this case can be established. In this work, uncertainty relations encompassing the triple components of angular momentum are derived. It has been shown that, compared with the relations involving only two components, a triple constant

often arises. Experimental verification is carried out on a single spin in diamond, and the results confirm the triple constant in a wide range of experimental parameters.

Experimental system and method

Experimental results by selecting two series of Bloch vectors

Recently, Bin Chen, postdoctor in department of physics (Co-Advisor: Gui-Lu Long ), cooperated with Prof. Jiangfeng Du and their experimental team from University of Science and Technology of China, derived tight uncertainty relations for the triple components of angular momentum in the spin-1/2 representation. The triple constant

exhibits its universality to some extent. The experimental demonstration with the single spin of an NV center consistently supports the theoretical results.

This work titled “Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum” has been published in Physical Review Letters [118, 180402 (2017)] on May 4, 2017. Bin Chen is an equally contributing author.