Control power in perfect controlled teleportation via partially entangled channels

TL;DR

This paper evaluates the control power in perfect controlled teleportation using three-qubit entangled channels, showing that partially entangled channels can outperform maximally entangled ones for certain state sets.

Contribution

It introduces a quantitative measure of controller's power, establishes bounds, and constructs partially entangled channels that surpass maximally entangled channels in controlled teleportation.

Findings

Maximally entangled GHZ state achieves optimal control power.

Partially entangled channels can exceed bounds for equatorial states.

Partially entangled channels outperform maximally entangled ones in specific scenarios.

Abstract

We analyze and evaluate perfect controlled teleportation via three-qubit entangled channels from the point of view of the controller. The key idea in controlled teleportation is that the teleportation is performed only with the participation of the controller. We calculate a quantitative measure of the controller's power and establish a lower bound on the control power required for controlled teleportation. We show that the maximally entangled GHZ state is a suitable channel for controlled teleportation of arbitrary single qubits - the controller's power meets the bound and the teleportation fidelity without the controller's permission is no better than the fidelity of a classical channel. We also construct partially entangled channels that exceed the bound for controlled teleportation of a restricted set of states called the equatorial states. We calculate the minimum entanglement required in these channels to exceed the bound. Moreover, we find that in these restricted controlled teleportation schemes, the partially entangled channels can outperform maximally entangled channels with respect to the controller's power. Our results provide a new perspective on controlled teleportation schemes and are of practical interest since we propose useful partially entangled channels.