Remote one-qubit state control by pure initial state of two-qubit sender. Selective-region- and eigenvalue-creation

TL;DR

This paper investigates remote control of a single-qubit mixed state via a two-qubit sender over spin chains, analyzing the effects of chain engineering on state creation, especially focusing on eigenvalue creation limits.

Contribution

It provides a detailed analysis of how chain engineering affects the ability to create specific receiver states, including eigenvalues, in remote quantum state transfer.

Findings

Complete state creation is possible only in chains engineered for perfect state transfer.

Homogeneous chains have limited state creation regions that decrease with length.

Eigenvalue creation is limited to chains of up to 34 nodes in homogeneous chains, extended to 68 with alternating chains.

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 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 creatable one and therefore deserves the special study. Regarding the homogeneous spin chain, an arbitrary eigenvalue can be created only if the chain is of no more then 34 nodes. Alternating chain allows us to increase this length up to 68 nodes.