Universal non-destructive estimation of quantum relative entropy

This paper describes the universal nondestructive estimation of quantum relative entropy. The sequences with the independent realizations of two i.i.d sources over a finite alphabet and the corresponding marginal distributions with the universal estimation is used to define the function quantum relative entropy. A product state emitted by a quantum i.i.d source with density matrix is subjected to a unitary transformation with a computational basis. The quantum entropy of a source and the eigenbasis without compromising the fidelity is learnt. With the arbitrary high accuracy the fidelity arbitrary is close to the unity