Optimal transfer of an unknown state via a bipartite operation

TL;DR

This paper introduces a measure called QST power to quantify the effectiveness of bipartite quantum operations in transferring unknown quantum states, providing analytical results especially for two-qubit systems.

Contribution

It defines the QST power as a measure for quantum state transfer capability and derives its properties and exact formulas for two-qubit unitaries.

Findings

QST power satisfies four key properties for bipartite operations.

Analytical expressions for QST power are provided for two-qubit systems.

Exact results are obtained for general two-qubit unitaries.

Abstract

A fundamental task in quantum information science is to transfer an unknown state from particle $A$ to particle $B$ (often in remote space locations) by using a bipartite quantum operation $\mathcal{E}^{AB}$. We suggest the power of $\mathcal{E}^{AB}$ for quantum state transfer (QST) to be the maximal average probability of QST over the initial states of particle $B$ and the identifications of the state vectors between $A$ and $B$. We find the QST power of a bipartite quantum operations satisfies four desired properties between two $d$-dimensional Hilbert spaces. When $A$ and $B$ are qubits, the analytical expressions of the QST power is given. In particular, we obtain the exact results of the QST power for a general two-qubit unitary transformation.