Dense coding capacity of a quantum channel

Riccardo Laurenza,Seth Lloyd,Stefano Pirandola,Cosmo Lupo

doi:10.1103/physrevresearch.2.023023

Abstract

We consider the fundamental protocol of dense coding of classical information assuming that noise affects both the forward and backward communication lines between Alice and Bob. Assuming that this noise is described by the same quantum channel, we define its dense coding capacity by optimizing over all adaptive strategies that Alice can implement, while Bob encodes the information by means of Pauli operators. Exploiting techniques of channel simulation and protocol stretching, we are able to establish the dense coding capacity of Pauli channels in arbitrary finite dimension, with simple formulas for depolarizing and dephasing qubit channels.

Highlights

Dense coding, known as superdense coding, has been one of the first examples of how quantum entanglement can boost information and communication technology [1]
In this work we have considered the most general adaptive protocol for the dense coding of classical information in a realistic scenario where noise affects both the communication lines between Alice and Bob
Assuming that this noise is modelled by the same quantum channel, we define its dense coding capacity as the maximum amount of classical information that Bob can transmit to Alice

Summary

INTRODUCTION

Known as superdense coding, has been one of the first examples of how quantum entanglement can boost information and communication technology [1]. Noise can affect the transmission of quantum systems from the sender (Bob) to the receiver (Alice), after the entangled resource state has been perfectly distributed This is the typical scenario in the definition of entanglement-assisted protocols whose capacity is known [18,19]. Bob may optimize his classical encoding strategy, i.e., the probability distribution of his Pauli encoders Optimizing over these protocols we define the dense coding capacity of a quantum channel between Alice and Bob. We use simulation techniques [23,24,25,26] that allow us to simplify the structure of the protocol and derive a single-letter upper bound for this capacity. This quantity is explicitly computed for a Pauli channel in arbitrary d dimension, with remarkably simple formulas for qubit channels, such as the depolarizing and the dephasing channel

DENSE CODING PROTOCOL

ADAPTIVE DENSE CODING

SINGLE-LETTER UPPER BOUND

DENSE CODING CAPACITY OF PAULI CHANNELS

CONCLUSION