Remote one-qubit-state control using the pure initial state of a two-qubit sender: Selective-region and eigenvalue creation

Abstract

We study the problem of remote one-qubit mixed state creation using a pure initial state of two-qubit sender and spin-1/2 chain as a connecting line. We express the parameters of creatable states in terms of transition amplitudes. We show that the creation of a complete receiver's state space can be achieved only in the chain engineered for the one-qubit perfect state transfer (PST) (for instance, in the fully engineered Ekert chain); the chain can be arbitrarily long in this case. As for the homogeneous chain, the creatable receiver's state region decreases quickly with the chain length. Both homogeneous chains and chains engineered for PST can be used for the purpose of selective state creation, when only the restricted part of the whole receiver's state space is of interest. Among the parameters of the receiver's state, the eigenvalue is the most hard to create and therefore deserves special study. Regarding the homogeneous spin chain, an arbitrary eigenvalue can be created only if the chain is of no more than 34 nodes. The alternating chain allows us to increase this length to up to 68 nodes.