Single-qubit peration sharing with Bell and W product states

TL;DR

This paper proposes two schemes for sharing a single-qubit operation remotely using shared entangled states, comparing their resource efficiency and success probabilities, with the second scheme being more effective and deterministic.

Contribution

It introduces two novel tripartite schemes utilizing Bell and W states for remote operation sharing, highlighting the advantages of asymmetric W states for deterministic success.

Findings

The second scheme achieves deterministic operation sharing.

The second scheme consumes fewer resources and has higher efficiency.

The first scheme is probabilistic and less resource-efficient.

Abstract

Two tripartite schemes are put forward with shared entanglements and LOCC for sharing an operation on a remote target sate. The first scheme uses a Bell and a symmetric W states as quantum channels, while the second replaces the symmetric W state by an asymmetric one. Both schemes are treated and compared from the aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that, the latter scheme is better than the former one. Particularly, the sharing can be achieved only probabilistically with the first scheme deterministically with the second one.