Entanglement-assisted quantum communication beating the quantum Singleton bound

Markus Grassl

doi:10.1103/physreva.103.l020601

Abstract

Brun, Devetak, and Hsieh [Science 314, 436 (2006)] demonstrated that preshared entanglement between the sender and receiver enables quantum communication protocols that have better parameters than schemes without the assistance of entanglement. Subsequently, the same authors derived a version of the so-called quantum Singleton bound that relates the parameters of the entanglement-assisted quantum-error-correcting codes proposed by them. We present an entanglement-assisted quantum communication scheme with parameters violating this bound in certain ranges. For a fixed transmission rate, our scheme allows one to correct a larger fraction of errors.

Highlights

Entanglement is a resource that enables or enhances many tasks in quantum communication
Independent of the dimension q of the subsystems, the parameters of a Quantum-error-correcting codes (QECCs) are constrained by the so-called quantum Singleton bound [4,13]
Our scheme beats the quantum Singleton bound (4) for quantum communication schemes with a rate below a certain threshold and uses a smaller amount c of entanglement than the scheme proposed in Ref. [6]

Summary

Introduction

Entanglement is a resource that enables or enhances many tasks in quantum communication. When the sender and receiver share a maximally entangled state, quantum teleportation allows the sender to transmit an unknown quantum state by just sending a finite amount of classical information over a noiseless classical channel [1]. The correspondence between entanglement distillation protocols and quantum-error-correcting codes in a communication scenario has been discussed in Ref. In this Letter we present a quantum communication scheme that uses a noisy quantum channel assisted by entanglement. The main idea is to execute a teleportation protocol in which the classical information is protected using a code and sent via the noisy quantum channel to the receiver. This allows one to use classical error-correcting codes.

MARKUS GRASSL

Codes meeting this bound with equality are called quantum