Perturbation of the numerical range of unitary matrices

In this work we show how to approach the problem of manimulating the numerical range of a unitary matrix. This task has farreaching impact on the study of discrimination of quantum measurements. We achieve the aforementioned manipulation by introducing
a method which allows us to find a unitary matrix whose numerical range contains the origin where at the same time the distance between
unitary matrix and its perturbation is relative small in given metric.