Controlled remote implementation of operations via graph states

TL;DR

This paper introduces protocols for controlled remote implementation of quantum operations using graph states, ensuring security, efficiency, and experimental feasibility with current technology.

Contribution

It presents a novel protocol for controlled remote quantum operation implementation utilizing graph states, emphasizing entanglement efficiency and control power verification.

Findings

Protocol achieves controlled remote operation with local operations and classical communication.

Entanglement cost is optimized for control function realization.

Control power is validated through positive operator valued measurement.

Abstract

We propose protocols for controlled remote implementation of operations with convincing control power. Sharing a $(2N+1)$-partite graph state, $2N$ participants collaborate to prepare the stator and realize the operation $\otimes_{j=1}^N\exp{[i\alpha_j\sigma_{n_{O_j}}]}$ on $N$ unknown states for distributed systems $O_j$, with the permission of a controller. All the implementation requirements of our protocol can be satisfied by means of local operations and classical communications, and the experimental feasibility is presented according to current techniques. We characterize the entanglement requirement of our protocol in terms of geometric measure of entanglement. It turns out to be economic to realize the control function from the perspective of entanglement cost. Further we show that the control power of our protocol is reliable by positive operator valued measurement.