Minimal control power of the controlled teleportation

TL;DR

This paper introduces the concept of minimal control power in controlled teleportation, generalizes it to multiqubit states, and analyzes its relation to entanglement, providing explicit calculations for GHZ and W states.

Contribution

It defines and computes the minimal control power for multiqubit states, linking it to entanglement measures and extending previous work on three-qubit states.

Findings

Standard GHZ and W states have maximal minimal control power.

Minimal control power correlates with three-qubit entanglement.

Explicit calculations for n-qubit GHZ and W states are provided.

Abstract

We generalize the control power of a perfect controlled teleportation of an entangled three-qubit pure state, suggested by Li and Ghose [Phys. Rev. A {\bf 90}, 052305 (2014)], to the control power of a general controlled teleportation of a multiqubit pure state. Thus, we define the minimal control power, and calculate the values of the minimal control power for a class of general three-qubit Greenberger-Horne-Zeilinger (GHZ) states and the three-qubit W class whose states have zero three-tangles. Moreover, we show that the standard three-qubit GHZ state and the standard three-qubit W state have the maximal values of the minimal control power for the two classes, respectively. This means that the minimal control power can be interpreted as not only an operational quantity of a three-qubit quantum communication but also a degree of three-qubit entanglement. In addition, we calculate the values of the minimal control power for general n-qubit GHZ states and the n-qubit W-type states.