Resource theory of Kirkwood-Dirac imaginarity

Abstract

As an extension of classical probability distribution, the Kirkwood-Dirac distribution (KDD) was discussed by Kirkwood in 1933 and Dirac 1945, independently. Recently, it has been proved that nonclassical values (negative and non-real values) of the KDD have the ability of outperforming their classical counterparts in quantum computation, quantum measurement and so on. In this work,
by dividing quantum states into KD-real (KD-free) and KD-imaginary (KD-resource) ones based on the KDD of a state, we establish a resource theory for KD-imaginarity with respect to a pair of bases $(A,B)$, {\color{blue}called the resource theory of Kirkwood-Dirac imaginarity. This theory} is different from the resource theory of imaginarity of quantum states with respect to one basis $A$, where the free states are those that have real density matrices under the basis $A$.