Remote creation of a one-qubit mixed state through a short homogeneous spin-1/2 chain

TL;DR

This paper presents a method for remotely creating a variety of one-qubit mixed states in a spin-1/2 chain using local control of the sender, enabling extensive state-space coverage and potential multi-sender sharing.

Contribution

It introduces a protocol for remote mixed state creation in a spin chain with local control, expanding the creatable state-space and enabling multi-sender sharing of states.

Findings

Large creatable regions can be achieved with a two-qubit sender.

Complete local control is possible at a fixed time instant.

The method allows sharing the receiver's state-space among multiple senders.

Abstract

We consider a method of remote mixed state creation of a one-qubit subsystem (receiver) in a spin-1/2 chain governed by the nearest-neighbor $XY$-Hamiltonian. Owing to the evolution of the chain along with the variable local unitary transformation of the one- or two-qubit sender, a large variety of receiver states can be created during some time interval starting with a fixed initial state of the whole quantum system. These states form the creatable region of the receiver's state-space. It is remarkable that, having the two-qubit sender, a large creatable region may be covered at a properly fixed time instant $t_0$ using just the variable local unitary transformation of the sender. In this case we have completely local control of the remote state creation. In general, for a given initial state, there are such receiver's states that may not be created using the above tool. These states form the unavailable region. In turn, this unavailable region might be the creatable region of another sender. Thus, in future, we have a way to share the whole receiver's state-space among the creatable regions of several senders. The effectiveness of remote state creation is characterized by the density function of the creatable region.