>My question is can you create a transformation of a quantum state, that from state |1>+|0> creates a state |0>+|1>.
You can verify that the operator |1><0| + |0><1| does this. This is simply the Pauli σ*_x_* matrix, in the standard basis.
>Add entanglement here, meaning from state |01>+|10> produces a state |11>+|00>?
In this case, you want the operator σ*_x_*⊗1. The σ*_x_* operates on the first qubit, interchanging 0 with 1 (and vice versa), and the 1 is the 2x2 identity matrix, which operates on the second qubit, and leaves its state unchanged.