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), 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.