Quantum cost of dense coding and teleportation

TL;DR

This paper analyzes the quantum cost of dense coding and teleportation protocols, revealing linear growth with dimension for dense coding and a fixed cost for teleportation, and relates cost to fidelity under noise.

Contribution

It provides explicit formulas for quantum cost in high-dimensional dense coding and teleportation, and links cost to fidelity in noisy environments.

Findings

Quantum cost of dense coding is d+3 for message (0,0) and d+4 for others.

Quantum cost of teleportation is fixed at 13 regardless of dimension.

Cost-fidelity relation established under four noise scenarios.

Abstract

The quantum cost is a key ingredient to evaluate the quality of quantum protocols from a practical viewpoint. We show that the quantum cost of d-dimensional dense coding protocol is equal to d+3 when transmitting the classical message (0,0), and that is equal to d+4 when transmitting other classical message. It appears linear growth with the dimension and thus makes sense for implementation. In contrast, the quantum cost of high-dimensional teleportation protocols is equal to 13, which is the maximum value of the cost for the two-dimensional case. As an application, we establish the relation between the quantum cost and fidelity of dense coding protocols in terms of four typical noise scenario.