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

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.

6 pages, 3 figures

References in corpus (12)

• Mixed State Entanglement and Quantum Error Correction
• Quantum secret sharing
• Teleportation, Bell's Inequalities and Inseparability
• Local environment can enhance fidelity of quantum teleportation
• Optimal Controlled Teleportation
• Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation
• Entanglement of three-qubit pure states in terms of teleportation capability
• Teleportation capability, distillability, and nonlocality on three-qubit states
• Genuine multipartite entanglement is not a precondition for secure conference key agreement
• Genuine multipartite entanglement measures based on multi-party teleportation capability
• Genuine Secret-Sharing States
• Quantum cryptographic resource distillation and entanglement