Operations with elements of transferred density matrix via unitary transformations at receiver side

Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following: turning some matrix elements to zero, rearranging the matrix elements and preparing their linear combinations with required coefficients. We also propose a protocol for solving a system of linear algebraic equations with a system of two equations as an example. Such operations are numerically simulated on the basis of 42-node spin-1/2 chain with the two-qubit sender and receiver.