Continuous-variable dense coding via a general Gaussian state: Monogamy relation

TL;DR

This paper explores continuous-variable dense coding using general Gaussian states, establishing conditions for quantum advantage and revealing a strict monogamy relation of entanglement in multipartite systems.

Contribution

It extends dense coding protocols to general Gaussian states and demonstrates a monogamy relation of operational entanglement based on communication capacity.

Findings

Quantum advantage achievable with general Gaussian states

Monogamy relation restricts quantum advantage to one pair in multipartite systems

Heisenberg's uncertainty principle underpins the monogamy of entanglement

Abstract

We study a continuous variable (CV) dense-coding protocol, originally proposed to employ a two-mode squeezed state, using a general two-mode Gaussian state as a quantum channel. We particularly obtain conditions to manifest quantum advantage by beating two well-known single-mode schemes, namely, the squeezed-state scheme (best Gaussian scheme) and the number-state scheme (optimal scheme achieving the Holevo bound). We then extend our study to a multipartite Gaussian state and investigate the monogamy of operational entanglement measured by the communication capacity under the dense-coding protocol. We show that this operational entanglement represents a strict monogamy relation, by means of Heisenberg's uncertainty principle among different parties, i.e., the quantum advantage for communication can be possible for only one pair of two-mode systems among many parties.