Optimization of remote one- and two-qubit state creation by unitary transformations of a sender and an extended receiver

We study the optimization problem for remote one- and two-qubit state creation via a homogeneous communication line of spin-$1/2$ particles using local unitary transformations of the multiqubit sender and extended receiver. We show that the maximum length of a communication line used for the needed state creation (the critical length) increases as the dimensionality of the sender and extended receiver increases. We use the model with the sender and extended receiver comprising up to ten qubits for the one-qubit state creation and consider the creation of two particular states, the almost pure state and the maximally mixed state. Regarding the two-qubit state creation, we numerically study the dependence of the critical length on a particular triad of independent eigenvalues to be created using the model with a four-qubit sender without an extended receiver.