Optimal super dense coding over noisy quantum channels

TL;DR

This paper analyzes the capacity of super dense coding over noisy quantum channels, identifying optimal states and encoding strategies, especially under Pauli and depolarizing noise, and demonstrating scenarios where non-unitary pre-processing enhances capacity.

Contribution

It derives the super dense coding capacity for noisy channels, explores the effect of noise thresholds on optimal initial states, and shows non-unitary pre-processing can improve information transfer.

Findings

Super dense coding capacity depends on noise level and initial resource state.

A threshold exists where maximally entangled states are optimal below it, and product states are better above.

Non-unitary pre-processing can increase the capacity compared to unitary encoding.

Abstract

We investigate super dense coding in the presence of noise, i.e. the subsystems of the entangled resource state have to pass a noisy unital quantum channel between the sender and the receiver. We discuss explicitly the case of Pauli channels in arbitrary dimension and derive the super dense coding capacity (i.e. the optimal information transfer) for some given resource states. We also study the case that the initial resource state can be chosen: for the qubit depolarizing channel we show that there is a threshold value for the noise parameter, below which the super dense coding protocol is optimized by a maximally entangled initial state, while above the threshold the dense coding capacity for any entangled initial state is smaller than the one for a product state. Finally, we provide an example of a noisy channel where non-unitary pre-processing increases the super dense coding capacity, as compared to only unitary encoding.