Investigating controlled teleportation capability of quantum states with respect to $k$-separability

TL;DR

This paper analyzes the limits of controlled teleportation fidelity based on the entanglement structure of quantum states, establishing thresholds for $k$-separable states and showing genuine multipartite entanglement isn't necessary for high performance.

Contribution

It extends teleportation fidelity thresholds to multi-party controlled schemes and clarifies the role of entanglement structure in teleportation capability.

Findings

Thresholds for $k$-separable states in controlled teleportation.

Genuine multipartite entanglement is not required for high teleportation fidelity.

Provides criteria for using quantum states as resources in controlled teleportation.

Abstract

Quantum teleportation is an essential application of quantum entanglement. The examination of teleportation fidelity in two-party standard teleportation schemes reveals a critical threshold distinguishing separable and entangled states. For separable states, their teleportation fidelities cannot exceed the threshold, emphasizing the significance of entanglement. We extend this analysis to multi-party scenarios known as controlled teleportation. Our study provides thresholds that $N$-qudit $k$-separable states cannot exceed in a controlled teleportation scheme, where $N \ge 3$ and $2 \le k \le N$. This not only establishes a standard for utilizing a given quantum state as a resource in controlled teleportation but also enhances our understanding of the influence of the entanglement structure on controlled teleportation performance. In addition, we show that genuine multipartite entanglement is not a prerequisite for achieving a high controlled teleportation capability.