Deterministic Quantum Dense Coding Networks

TL;DR

This paper investigates the potential of multipartite quantum states, such as gGHZ, gW, and Dicke states, to enable deterministic dense coding networks, revealing that certain states can surpass classical limits.

Contribution

It identifies which multipartite states can be used for deterministic dense coding, showing that gGHZ states are generally not beneficial except for the GHZ state, while gW and Dicke states can provide advantages.

Findings

gGHZ states are not beneficial for deterministic dense coding beyond classical limits, except GHZ.

gW and Dicke states can enable quantum advantage in deterministic dense coding.

Numerical simulations show higher density of deterministic codeable states in GHZ-class than W-class.

Abstract

We consider the scenario of deterministic classical information transmission between multiple senders and a single receiver, when they a priori share a multipartite quantum state -- an attempt towards building a deterministic dense coding network. Specifically, we prove that in the case of two or three senders and a single receiver, generalized Greenberger-Horne-Zeilinger (gGHZ) states are not beneficial for sending classical information deterministically beyond the classical limit, except when the shared state is the GHZ state itself. On the other hand, three- and four-qubit generalized W (gW) states with specific parameters as well as the four-qubit Dicke states can provide a quantum advantage of sending the information in deterministic dense coding. Interestingly however, numerical simulations in the three-qubit scenario reveal that the percentage of states from the GHZ-class that are deterministic dense codeable is higher than that of states from the W-class.